[{"issue":"6","year":"2025","publisher":"Elsevier","date_created":"2024-10-22T09:31:19Z","title":"Multiresolution analysis on spectra of hermitian matrices","publication":"Indagationes Mathematicae","abstract":[{"text":"We establish a multiresolution analysis on the space $\\text{Herm}(n)$ of\r\n$n\\times n$ complex Hermitian matrices which is adapted to invariance under\r\nconjugation by the unitary group $U(n).$ The orbits under this action are\r\nparametrized by the possible ordered spectra of Hermitian matrices, which\r\nconstitute a closed Weyl chamber of type $A_{n-1}$ in $\\mathbb R^n.$ The space\r\n$L^2(\\text{Herm}(n))^{U(n)}$ of radial, i.e. $U(n)$-invariant $L^2$-functions\r\non $\\text{Herm}(n)$ is naturally identified with a certain weighted $L^2$-space\r\non this chamber.\r\n  The scale spaces of our multiresolution analysis are obtained by usual dyadic\r\ndilations as well as generalized translations of a scaling function, where the\r\ngeneralized translation is a hypergroup translation which respects the radial\r\ngeometry. We provide a concise criterion to characterize orthonormal wavelet\r\nbases and show that such bases always exist. They provide natural orthonormal\r\nbases of the space $L^2(\\text{Herm}(n))^{U(n)}.$\r\n  Furthermore, we show how to obtain radial scaling functions from classical\r\nscaling functions on $\\mathbb R^{n}$. Finally, generalizations related to the\r\nCartan decompositions for general compact Lie groups are indicated.","lang":"eng"}],"file":[{"relation":"main_file","success":1,"content_type":"application/pdf","file_name":"MSA_hermitsch_published.pdf","access_level":"closed","file_id":"64288","file_size":443262,"creator":"llangen","date_created":"2026-02-19T14:14:39Z","date_updated":"2026-02-19T14:14:39Z"}],"external_id":{"arxiv":["2410.10364"]},"ddc":["510"],"language":[{"iso":"eng"}],"publication_status":"published","has_accepted_license":"1","related_material":{"link":[{"url":"https://arxiv.org/abs/2410.10364","relation":"research_paper"}]},"citation":{"ama":"Langen L, Rösler M. Multiresolution analysis on spectra of hermitian matrices. <i>Indagationes Mathematicae</i>. 2025;36(6):1671-1694.","chicago":"Langen, Lukas, and Margit Rösler. “Multiresolution Analysis on Spectra of Hermitian Matrices.” <i>Indagationes Mathematicae</i> 36, no. 6 (2025): 1671–94.","ieee":"L. Langen and M. Rösler, “Multiresolution analysis on spectra of hermitian matrices,” <i>Indagationes Mathematicae</i>, vol. 36, no. 6, pp. 1671–1694, 2025.","apa":"Langen, L., &#38; Rösler, M. (2025). Multiresolution analysis on spectra of hermitian matrices. <i>Indagationes Mathematicae</i>, <i>36</i>(6), 1671–1694.","mla":"Langen, Lukas, and Margit Rösler. “Multiresolution Analysis on Spectra of Hermitian Matrices.” <i>Indagationes Mathematicae</i>, vol. 36, no. 6, Elsevier, 2025, pp. 1671–94.","bibtex":"@article{Langen_Rösler_2025, title={Multiresolution analysis on spectra of hermitian matrices}, volume={36}, number={6}, journal={Indagationes Mathematicae}, publisher={Elsevier}, author={Langen, Lukas and Rösler, Margit}, year={2025}, pages={1671–1694} }","short":"L. Langen, M. Rösler, Indagationes Mathematicae 36 (2025) 1671–1694."},"page":"1671-1694","intvolume":"        36","date_updated":"2026-02-19T14:16:43Z","author":[{"first_name":"Lukas","last_name":"Langen","full_name":"Langen, Lukas","id":"73664"},{"last_name":"Rösler","id":"37390","full_name":"Rösler, Margit","first_name":"Margit"}],"volume":36,"main_file_link":[{"url":"https://doi.org/10.1016/j.indag.2025.03.009"}],"type":"journal_article","status":"public","project":[{"name":"TRR 358 - Ganzzahlige Strukturen in Geometrie und Darstellungstheorie","_id":"357"}],"_id":"56717","user_id":"73664","department":[{"_id":"555"}],"article_type":"original","file_date_updated":"2026-02-19T14:14:39Z"},{"publication":"Indagationes Mathematicae","type":"journal_article","status":"public","abstract":[{"text":"We study the asymptotic behaviour of Bessel functions associated of root\r\nsystems of type $A_{n-1}$ and type $B_n$ with positive multiplicities as the\r\nrank $n$ tends to infinity. In both cases, we characterize the possible limit\r\nfunctions and the Vershik-Kerov type sequences of spectral parameters for which\r\nsuch limits exist. In the type $A$ case, this gives a new and very natural\r\napproach to recent results by Assiotis and Najnudel in the context of\r\n$\\beta$-ensembles in random matrix theory. These results generalize known facts\r\nabout the approximation of the (positive-definite) Olshanski spherical\r\nfunctions of the space of infinite-dimensional Hermitian matrices over $\\mathbb\r\nF = \\mathbb R, \\mathbb C, \\mathbb H$ (with the action of the associated\r\ninfinite unitary group) by spherical functions of finite-dimensional spaces of\r\nHermitian matrices. In the type B case, our results include asymptotic results\r\nfor the spherical functions associated with the Cartan motion groups of\r\nnon-compact Grassmannians as the rank goes to infinity, and a classification of\r\nthe Olshanski spherical functions of the associated inductive limits.","lang":"eng"}],"user_id":"82981","_id":"54820","language":[{"iso":"eng"}],"publication_status":"epub_ahead","citation":{"chicago":"Brennecken, Dominik, and Margit Rösler. “Limits of Bessel Functions for Root Systems as the Rank Tends to  Infinity.” <i>Indagationes Mathematicae</i>, 2024. <a href=\"https://doi.org/10.1016/j.indag.2024.05.004\">https://doi.org/10.1016/j.indag.2024.05.004</a>.","ieee":"D. Brennecken and M. Rösler, “Limits of Bessel functions for root systems as the rank tends to  infinity,” <i>Indagationes Mathematicae</i>, 2024, doi: <a href=\"https://doi.org/10.1016/j.indag.2024.05.004\">10.1016/j.indag.2024.05.004</a>.","ama":"Brennecken D, Rösler M. Limits of Bessel functions for root systems as the rank tends to  infinity. <i>Indagationes Mathematicae</i>. Published online 2024. doi:<a href=\"https://doi.org/10.1016/j.indag.2024.05.004\">10.1016/j.indag.2024.05.004</a>","apa":"Brennecken, D., &#38; Rösler, M. (2024). Limits of Bessel functions for root systems as the rank tends to  infinity. <i>Indagationes Mathematicae</i>. <a href=\"https://doi.org/10.1016/j.indag.2024.05.004\">https://doi.org/10.1016/j.indag.2024.05.004</a>","mla":"Brennecken, Dominik, and Margit Rösler. “Limits of Bessel Functions for Root Systems as the Rank Tends to  Infinity.” <i>Indagationes Mathematicae</i>, Elsevier, 2024, doi:<a href=\"https://doi.org/10.1016/j.indag.2024.05.004\">10.1016/j.indag.2024.05.004</a>.","bibtex":"@article{Brennecken_Rösler_2024, title={Limits of Bessel functions for root systems as the rank tends to  infinity}, DOI={<a href=\"https://doi.org/10.1016/j.indag.2024.05.004\">10.1016/j.indag.2024.05.004</a>}, journal={Indagationes Mathematicae}, publisher={Elsevier}, author={Brennecken, Dominik and Rösler, Margit}, year={2024} }","short":"D. Brennecken, M. Rösler, Indagationes Mathematicae (2024)."},"year":"2024","author":[{"first_name":"Dominik","id":"55911","full_name":"Brennecken, Dominik","last_name":"Brennecken"},{"first_name":"Margit","last_name":"Rösler","id":"37390","full_name":"Rösler, Margit"}],"date_created":"2024-06-19T08:46:08Z","publisher":"Elsevier","date_updated":"2024-07-15T09:09:55Z","doi":"10.1016/j.indag.2024.05.004","title":"Limits of Bessel functions for root systems as the rank tends to  infinity"},{"publication_status":"published","publication_identifier":{"isbn":["978-3-031-57004-9"]},"citation":{"ieee":"D. Brennecken and M. Rösler, “The Laplace transform in Dunkl theory,” in <i>Women in Analysis and PDE</i>, vol. 5, M. Chatzakou, M. Ruzhansky, and D. Stoeva, Eds. Birkhäuser Cham, 2024, p. 425.","chicago":"Brennecken, Dominik, and Margit Rösler. “The Laplace Transform in Dunkl Theory.” In <i>Women in Analysis and PDE</i>, edited by Marianna Chatzakou, Michael Ruzhansky, and Diana Stoeva, 5:425. Trends in Mathematics: Research Perspectives Ghent Analysis and PDE Cente. Birkhäuser Cham, 2024.","ama":"Brennecken D, Rösler M. The Laplace transform in Dunkl theory. In: Chatzakou M, Ruzhansky M, Stoeva D, eds. <i>Women in Analysis and PDE</i>. Vol 5. Trends in Mathematics: Research Perspectives Ghent Analysis and PDE Cente. Birkhäuser Cham; 2024:425.","apa":"Brennecken, D., &#38; Rösler, M. (2024). The Laplace transform in Dunkl theory. In M. Chatzakou, M. Ruzhansky, &#38; D. Stoeva (Eds.), <i>Women in Analysis and PDE</i> (Vol. 5, p. 425). Birkhäuser Cham.","mla":"Brennecken, Dominik, and Margit Rösler. “The Laplace Transform in Dunkl Theory.” <i>Women in Analysis and PDE</i>, edited by Marianna Chatzakou et al., vol. 5, Birkhäuser Cham, 2024, p. 425.","bibtex":"@inbook{Brennecken_Rösler_2024, series={Trends in Mathematics: Research Perspectives Ghent Analysis and PDE Cente}, title={The Laplace transform in Dunkl theory}, volume={5}, booktitle={Women in Analysis and PDE}, publisher={Birkhäuser Cham}, author={Brennecken, Dominik and Rösler, Margit}, editor={Chatzakou, Marianna and Ruzhansky, Michael and Stoeva, Diana}, year={2024}, pages={425}, collection={Trends in Mathematics: Research Perspectives Ghent Analysis and PDE Cente} }","short":"D. Brennecken, M. Rösler, in: M. Chatzakou, M. Ruzhansky, D. Stoeva (Eds.), Women in Analysis and PDE, Birkhäuser Cham, 2024, p. 425."},"page":"425","intvolume":"         5","year":"2024","date_created":"2024-09-03T15:31:27Z","author":[{"first_name":"Dominik","id":"55911","full_name":"Brennecken, Dominik","last_name":"Brennecken"},{"id":"37390","full_name":"Rösler, Margit","last_name":"Rösler","first_name":"Margit"}],"volume":5,"date_updated":"2024-09-05T06:58:54Z","publisher":"Birkhäuser Cham","title":"The Laplace transform in Dunkl theory","type":"book_chapter","publication":"Women in Analysis and PDE","status":"public","editor":[{"full_name":"Chatzakou, Marianna","last_name":"Chatzakou","first_name":"Marianna"},{"full_name":"Ruzhansky, Michael","last_name":"Ruzhansky","first_name":"Michael"},{"last_name":"Stoeva","full_name":"Stoeva, Diana","first_name":"Diana"}],"series_title":"Trends in Mathematics: Research Perspectives Ghent Analysis and PDE Cente","user_id":"82981","department":[{"_id":"555"}],"_id":"56001","language":[{"iso":"eng"}]},{"publication":"Transactions of the American Mathematical Society","type":"journal_article","status":"public","department":[{"_id":"555"}],"user_id":"37390","_id":"36294","language":[{"iso":"eng"}],"issue":"4","publication_status":"published","page":"2419-2447","intvolume":"       376","citation":{"ieee":"D. Brennecken and M. Rösler, “The Dunkl-Laplace transform and Macdonald’s hypergeometric series,” <i>Transactions of the American Mathematical Society</i>, vol. 376, no. 4, pp. 2419–2447, 2023, doi: <a href=\"https://doi.org/10.1090/tran/8860\">10.1090/tran/8860</a>.","chicago":"Brennecken, Dominik, and Margit Rösler. “The Dunkl-Laplace Transform and Macdonald’s Hypergeometric Series.” <i>Transactions of the American Mathematical Society</i> 376, no. 4 (2023): 2419–47. <a href=\"https://doi.org/10.1090/tran/8860\">https://doi.org/10.1090/tran/8860</a>.","ama":"Brennecken D, Rösler M. The Dunkl-Laplace transform and Macdonald’s hypergeometric series. <i>Transactions of the American Mathematical Society</i>. 2023;376(4):2419-2447. doi:<a href=\"https://doi.org/10.1090/tran/8860\">10.1090/tran/8860</a>","bibtex":"@article{Brennecken_Rösler_2023, title={The Dunkl-Laplace transform and Macdonald’s hypergeometric series}, volume={376}, DOI={<a href=\"https://doi.org/10.1090/tran/8860\">10.1090/tran/8860</a>}, number={4}, journal={Transactions of the American Mathematical Society}, publisher={ American Mathematical Society}, author={Brennecken, Dominik and Rösler, Margit}, year={2023}, pages={2419–2447} }","mla":"Brennecken, Dominik, and Margit Rösler. “The Dunkl-Laplace Transform and Macdonald’s Hypergeometric Series.” <i>Transactions of the American Mathematical Society</i>, vol. 376, no. 4,  American Mathematical Society, 2023, pp. 2419–47, doi:<a href=\"https://doi.org/10.1090/tran/8860\">10.1090/tran/8860</a>.","short":"D. Brennecken, M. Rösler, Transactions of the American Mathematical Society 376 (2023) 2419–2447.","apa":"Brennecken, D., &#38; Rösler, M. (2023). The Dunkl-Laplace transform and Macdonald’s hypergeometric series. <i>Transactions of the American Mathematical Society</i>, <i>376</i>(4), 2419–2447. <a href=\"https://doi.org/10.1090/tran/8860\">https://doi.org/10.1090/tran/8860</a>"},"year":"2023","volume":376,"date_created":"2023-01-12T08:32:44Z","author":[{"last_name":"Brennecken","full_name":"Brennecken, Dominik","id":"55911","first_name":"Dominik"},{"last_name":"Rösler","id":"37390","full_name":"Rösler, Margit","first_name":"Margit"}],"date_updated":"2024-04-24T12:47:49Z","publisher":" American Mathematical Society","doi":"10.1090/tran/8860","title":"The Dunkl-Laplace transform and Macdonald’s hypergeometric series"},{"date_updated":"2023-01-24T22:16:21Z","date_created":"2023-01-23T08:31:27Z","author":[{"id":"37390","full_name":"Rösler, Margit","last_name":"Rösler","first_name":"Margit"},{"first_name":"Michael","last_name":"Voit","full_name":"Voit, Michael"}],"title":"Elementary symmetric polynomials and martingales for Heckman-Opdam processes","conference":{"name":"Hypergeometry, integrability and Lie theory"},"doi":"10.48550/ARXIV.2108.03228","publication_status":"published","issue":"780","year":"2022","page":"243-262","citation":{"apa":"Rösler, M., &#38; Voit, M. (2022). Elementary symmetric polynomials and martingales for Heckman-Opdam processes. <i>Contemporary Mathematics</i>, <i>780</i>, 243–262. <a href=\"https://doi.org/10.48550/ARXIV.2108.03228\">https://doi.org/10.48550/ARXIV.2108.03228</a>","mla":"Rösler, Margit, and Michael Voit. “Elementary Symmetric Polynomials and Martingales for Heckman-Opdam Processes.” <i>Contemporary Mathematics</i>, no. 780, 2022, pp. 243–62, doi:<a href=\"https://doi.org/10.48550/ARXIV.2108.03228\">10.48550/ARXIV.2108.03228</a>.","bibtex":"@article{Rösler_Voit_2022, title={Elementary symmetric polynomials and martingales for Heckman-Opdam processes}, DOI={<a href=\"https://doi.org/10.48550/ARXIV.2108.03228\">10.48550/ARXIV.2108.03228</a>}, number={780}, journal={Contemporary Mathematics}, author={Rösler, Margit and Voit, Michael}, year={2022}, pages={243–262} }","short":"M. Rösler, M. Voit, Contemporary Mathematics (2022) 243–262.","ama":"Rösler M, Voit M. Elementary symmetric polynomials and martingales for Heckman-Opdam processes. <i>Contemporary Mathematics</i>. 2022;(780):243-262. doi:<a href=\"https://doi.org/10.48550/ARXIV.2108.03228\">10.48550/ARXIV.2108.03228</a>","ieee":"M. Rösler and M. Voit, “Elementary symmetric polynomials and martingales for Heckman-Opdam processes,” <i>Contemporary Mathematics</i>, no. 780, pp. 243–262, 2022, doi: <a href=\"https://doi.org/10.48550/ARXIV.2108.03228\">10.48550/ARXIV.2108.03228</a>.","chicago":"Rösler, Margit, and Michael Voit. “Elementary Symmetric Polynomials and Martingales for Heckman-Opdam Processes.” <i>Contemporary Mathematics</i>, no. 780 (2022): 243–62. <a href=\"https://doi.org/10.48550/ARXIV.2108.03228\">https://doi.org/10.48550/ARXIV.2108.03228</a>."},"_id":"38039","department":[{"_id":"555"}],"user_id":"37390","language":[{"iso":"eng"}],"publication":"Contemporary Mathematics","type":"journal_article","abstract":[{"lang":"eng","text":"We consider the generators $L_k$ of Heckman-Opdam diffusion processes in the compact and non-compact case in $N$ dimensions for root systems of type $A$ and $B$, with a multiplicity function of the form $k=κk_0$ with some fixed value $k_0$ and a varying constant $κ\\in\\,[0,\\infty[$. Using elementary symmetric functions, we present polynomials which are simultaneous eigenfunctions of the $L_k$ for all $κ\\in\\,]0,\\infty[$. This leads to martingales associated with the Heckman-Opdam diffusions $ (X_{t,1},\\ldots,X_{t,N})_{t\\ge0}$. As our results extend to the freezing case $κ=\\infty$ with a deterministic limit after some renormalization, we find formulas for the expectations $\\mathbb E(\\prod_{j=1}^N(y-X_{t,j})),$ $y\\in\\mathbb C$."}],"status":"public"},{"date_updated":"2023-01-24T22:16:12Z","publisher":"Oxford University Press (OUP)","author":[{"first_name":"Margit","full_name":"Rösler, Margit","id":"37390","last_name":"Rösler"},{"last_name":"Voit","full_name":"Voit, Michael","first_name":"Michael"}],"date_created":"2023-01-20T08:50:07Z","volume":2021,"title":"Sonine Formulas and Intertwining Operators in Dunkl Theory","doi":"10.1093/imrn/rnz313","publication_status":"published","publication_identifier":{"issn":["1073-7928","1687-0247"]},"issue":"17","year":"2021","citation":{"bibtex":"@article{Rösler_Voit_2021, title={Sonine Formulas and Intertwining Operators in Dunkl Theory}, volume={2021}, DOI={<a href=\"https://doi.org/10.1093/imrn/rnz313\">10.1093/imrn/rnz313</a>}, number={17}, journal={International Mathematics Research Notices}, publisher={Oxford University Press (OUP)}, author={Rösler, Margit and Voit, Michael}, year={2021}, pages={13202–13230} }","short":"M. Rösler, M. Voit, International Mathematics Research Notices 2021 (2021) 13202–13230.","mla":"Rösler, Margit, and Michael Voit. “Sonine Formulas and Intertwining Operators in Dunkl Theory.” <i>International Mathematics Research Notices</i>, vol. 2021, no. 17, Oxford University Press (OUP), 2021, pp. 13202–30, doi:<a href=\"https://doi.org/10.1093/imrn/rnz313\">10.1093/imrn/rnz313</a>.","apa":"Rösler, M., &#38; Voit, M. (2021). Sonine Formulas and Intertwining Operators in Dunkl Theory. <i>International Mathematics Research Notices</i>, <i>2021</i>(17), 13202–13230. <a href=\"https://doi.org/10.1093/imrn/rnz313\">https://doi.org/10.1093/imrn/rnz313</a>","ama":"Rösler M, Voit M. Sonine Formulas and Intertwining Operators in Dunkl Theory. <i>International Mathematics Research Notices</i>. 2021;2021(17):13202-13230. doi:<a href=\"https://doi.org/10.1093/imrn/rnz313\">10.1093/imrn/rnz313</a>","chicago":"Rösler, Margit, and Michael Voit. “Sonine Formulas and Intertwining Operators in Dunkl Theory.” <i>International Mathematics Research Notices</i> 2021, no. 17 (2021): 13202–30. <a href=\"https://doi.org/10.1093/imrn/rnz313\">https://doi.org/10.1093/imrn/rnz313</a>.","ieee":"M. Rösler and M. Voit, “Sonine Formulas and Intertwining Operators in Dunkl Theory,” <i>International Mathematics Research Notices</i>, vol. 2021, no. 17, pp. 13202–13230, 2021, doi: <a href=\"https://doi.org/10.1093/imrn/rnz313\">10.1093/imrn/rnz313</a>."},"intvolume":"      2021","page":"13202-13230","_id":"37649","user_id":"37390","keyword":["General Mathematics"],"language":[{"iso":"eng"}],"type":"journal_article","publication":"International Mathematics Research Notices","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title>\r\n               <jats:p>Let $V_k$ denote Dunkl’s intertwining operator associated with some root system $R$ and multiplicity $k$. For two multiplicities $k, k^{\\prime }$ on $R$, we study the intertwiner $V_{k^{\\prime },k} = V_{k^{\\prime }}\\circ V_k^{-1}$ between Dunkl operators with multiplicities $k$ and $k^{\\prime }.$ It has been a long-standing conjecture that $V_{k^{\\prime },k}$ is positive if $k^{\\prime } \\geq k \\geq 0.$ We disprove this conjecture by constructing counterexamples for root system $B_n$. This matter is closely related to the existence of Sonine-type integral representations between Dunkl kernels and Bessel functions with different multiplicities. In our examples, such Sonine formulas do not exist. As a consequence, we obtain necessary conditions on Sonine formulas for Heckman–Opdam hypergeometric functions of type $BC_n$ and conditions for positive branching coefficients between multivariable Jacobi polynomials.</jats:p>"}],"status":"public"},{"language":[{"iso":"eng"}],"keyword":["Applied Mathematics","General Mathematics"],"department":[{"_id":"555"}],"user_id":"37390","_id":"37659","status":"public","publication":"Proceedings of the American Mathematical Society","type":"journal_article","doi":"10.1090/proc/15312","title":"Positive intertwiners for Bessel functions of type B","volume":149,"author":[{"id":"37390","full_name":"Rösler, Margit","last_name":"Rösler","first_name":"Margit"},{"first_name":"Michael","last_name":"Voit","full_name":"Voit, Michael"}],"date_created":"2023-01-20T09:22:12Z","date_updated":"2023-01-24T22:16:16Z","publisher":"American Mathematical Society (AMS)","intvolume":"       149","page":"1151-1163","citation":{"ama":"Rösler M, Voit M. Positive intertwiners for Bessel functions of type B. <i>Proceedings of the American Mathematical Society</i>. 2021;149(3):1151-1163. doi:<a href=\"https://doi.org/10.1090/proc/15312\">10.1090/proc/15312</a>","chicago":"Rösler, Margit, and Michael Voit. “Positive Intertwiners for Bessel Functions of Type B.” <i>Proceedings of the American Mathematical Society</i> 149, no. 3 (2021): 1151–63. <a href=\"https://doi.org/10.1090/proc/15312\">https://doi.org/10.1090/proc/15312</a>.","ieee":"M. Rösler and M. Voit, “Positive intertwiners for Bessel functions of type B,” <i>Proceedings of the American Mathematical Society</i>, vol. 149, no. 3, pp. 1151–1163, 2021, doi: <a href=\"https://doi.org/10.1090/proc/15312\">10.1090/proc/15312</a>.","mla":"Rösler, Margit, and Michael Voit. “Positive Intertwiners for Bessel Functions of Type B.” <i>Proceedings of the American Mathematical Society</i>, vol. 149, no. 3, American Mathematical Society (AMS), 2021, pp. 1151–63, doi:<a href=\"https://doi.org/10.1090/proc/15312\">10.1090/proc/15312</a>.","short":"M. Rösler, M. Voit, Proceedings of the American Mathematical Society 149 (2021) 1151–1163.","bibtex":"@article{Rösler_Voit_2021, title={Positive intertwiners for Bessel functions of type B}, volume={149}, DOI={<a href=\"https://doi.org/10.1090/proc/15312\">10.1090/proc/15312</a>}, number={3}, journal={Proceedings of the American Mathematical Society}, publisher={American Mathematical Society (AMS)}, author={Rösler, Margit and Voit, Michael}, year={2021}, pages={1151–1163} }","apa":"Rösler, M., &#38; Voit, M. (2021). Positive intertwiners for Bessel functions of type B. <i>Proceedings of the American Mathematical Society</i>, <i>149</i>(3), 1151–1163. <a href=\"https://doi.org/10.1090/proc/15312\">https://doi.org/10.1090/proc/15312</a>"},"year":"2021","issue":"3","publication_identifier":{"issn":["0002-9939","1088-6826"]},"publication_status":"published"},{"publisher":"Elsevier BV","date_updated":"2023-01-24T22:16:07Z","volume":278,"date_created":"2023-01-20T09:22:53Z","author":[{"first_name":"Margit","last_name":"Rösler","id":"37390","full_name":"Rösler, Margit"}],"title":"Riesz distributions and Laplace transform in the Dunkl setting of type A","doi":"10.1016/j.jfa.2020.108506","publication_identifier":{"issn":["0022-1236"]},"publication_status":"published","issue":"12","year":"2020","intvolume":"       278","citation":{"ieee":"M. Rösler, “Riesz distributions and Laplace transform in the Dunkl setting of type A,” <i>Journal of Functional Analysis</i>, vol. 278, no. 12, Art. no. 108506, 2020, doi: <a href=\"https://doi.org/10.1016/j.jfa.2020.108506\">10.1016/j.jfa.2020.108506</a>.","chicago":"Rösler, Margit. “Riesz Distributions and Laplace Transform in the Dunkl Setting of Type A.” <i>Journal of Functional Analysis</i> 278, no. 12 (2020). <a href=\"https://doi.org/10.1016/j.jfa.2020.108506\">https://doi.org/10.1016/j.jfa.2020.108506</a>.","ama":"Rösler M. Riesz distributions and Laplace transform in the Dunkl setting of type A. <i>Journal of Functional Analysis</i>. 2020;278(12). doi:<a href=\"https://doi.org/10.1016/j.jfa.2020.108506\">10.1016/j.jfa.2020.108506</a>","short":"M. Rösler, Journal of Functional Analysis 278 (2020).","mla":"Rösler, Margit. “Riesz Distributions and Laplace Transform in the Dunkl Setting of Type A.” <i>Journal of Functional Analysis</i>, vol. 278, no. 12, 108506, Elsevier BV, 2020, doi:<a href=\"https://doi.org/10.1016/j.jfa.2020.108506\">10.1016/j.jfa.2020.108506</a>.","bibtex":"@article{Rösler_2020, title={Riesz distributions and Laplace transform in the Dunkl setting of type A}, volume={278}, DOI={<a href=\"https://doi.org/10.1016/j.jfa.2020.108506\">10.1016/j.jfa.2020.108506</a>}, number={12108506}, journal={Journal of Functional Analysis}, publisher={Elsevier BV}, author={Rösler, Margit}, year={2020} }","apa":"Rösler, M. (2020). Riesz distributions and Laplace transform in the Dunkl setting of type A. <i>Journal of Functional Analysis</i>, <i>278</i>(12), Article 108506. <a href=\"https://doi.org/10.1016/j.jfa.2020.108506\">https://doi.org/10.1016/j.jfa.2020.108506</a>"},"_id":"37660","department":[{"_id":"555"}],"user_id":"93826","keyword":["Analysis"],"article_number":"108506","language":[{"iso":"eng"}],"publication":"Journal of Functional Analysis","type":"journal_article","status":"public"},{"title":"Beta Distributions and Sonine Integrals for Bessel Functions on Symmetric Cones","doi":"10.1111/sapm.12217","date_updated":"2023-01-24T22:15:51Z","publisher":"Wiley","volume":141,"author":[{"first_name":"Margit","full_name":"Rösler, Margit","id":"37390","last_name":"Rösler"},{"last_name":"Voit","full_name":"Voit, Michael","first_name":"Michael"}],"date_created":"2023-01-20T09:24:36Z","year":"2018","intvolume":"       141","page":"474-500","citation":{"chicago":"Rösler, Margit, and Michael Voit. “Beta Distributions and Sonine Integrals for Bessel Functions on Symmetric Cones.” <i>Studies in Applied Mathematics</i> 141, no. 4 (2018): 474–500. <a href=\"https://doi.org/10.1111/sapm.12217\">https://doi.org/10.1111/sapm.12217</a>.","ieee":"M. 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Beta Distributions and Sonine Integrals for Bessel Functions on Symmetric Cones. <i>Studies in Applied Mathematics</i>, <i>141</i>(4), 474–500. <a href=\"https://doi.org/10.1111/sapm.12217\">https://doi.org/10.1111/sapm.12217</a>","mla":"Rösler, Margit, and Michael Voit. “Beta Distributions and Sonine Integrals for Bessel Functions on Symmetric Cones.” <i>Studies in Applied Mathematics</i>, vol. 141, no. 4, Wiley, 2018, pp. 474–500, doi:<a href=\"https://doi.org/10.1111/sapm.12217\">10.1111/sapm.12217</a>.","bibtex":"@article{Rösler_Voit_2018, title={Beta Distributions and Sonine Integrals for Bessel Functions on Symmetric Cones}, volume={141}, DOI={<a href=\"https://doi.org/10.1111/sapm.12217\">10.1111/sapm.12217</a>}, number={4}, journal={Studies in Applied Mathematics}, publisher={Wiley}, author={Rösler, Margit and Voit, Michael}, year={2018}, pages={474–500} }","short":"M. Rösler, M. Voit, Studies in Applied Mathematics 141 (2018) 474–500."},"publication_identifier":{"issn":["0022-2526"]},"publication_status":"published","issue":"4","keyword":["Applied Mathematics"],"language":[{"iso":"eng"}],"alternative_title":["Beta Distributions and Sonine Integrals"],"_id":"37661","department":[{"_id":"555"}],"user_id":"93826","status":"public","publication":"Studies in Applied Mathematics","type":"journal_article"},{"title":"On the Green Function and Poisson Integrals of the Dunkl Laplacian","doi":"10.1007/s11118-017-9638-6","date_updated":"2023-01-24T22:16:02Z","publisher":"Springer Science and Business Media LLC","volume":48,"date_created":"2023-01-20T09:25:41Z","author":[{"last_name":"Rösler","full_name":"Rösler, Margit","id":"37390","first_name":"Margit"},{"first_name":"Piotr","last_name":"Graczyk","full_name":"Graczyk, Piotr"},{"full_name":"Luks, Tomasz","last_name":"Luks","first_name":"Tomasz"}],"year":"2018","intvolume":"        48","page":"337-360","citation":{"bibtex":"@article{Rösler_Graczyk_Luks_2018, title={On the Green Function and Poisson Integrals of the Dunkl Laplacian}, volume={48}, DOI={<a href=\"https://doi.org/10.1007/s11118-017-9638-6\">10.1007/s11118-017-9638-6</a>}, number={3}, journal={Potential Analysis}, publisher={Springer Science and Business Media LLC}, author={Rösler, Margit and Graczyk, Piotr and Luks, Tomasz}, year={2018}, pages={337–360} }","mla":"Rösler, Margit, et al. “On the Green Function and Poisson Integrals of the Dunkl Laplacian.” <i>Potential Analysis</i>, vol. 48, no. 3, Springer Science and Business Media LLC, 2018, pp. 337–60, doi:<a href=\"https://doi.org/10.1007/s11118-017-9638-6\">10.1007/s11118-017-9638-6</a>.","short":"M. Rösler, P. Graczyk, T. Luks, Potential Analysis 48 (2018) 337–360.","apa":"Rösler, M., Graczyk, P., &#38; Luks, T. (2018). On the Green Function and Poisson Integrals of the Dunkl Laplacian. <i>Potential Analysis</i>, <i>48</i>(3), 337–360. <a href=\"https://doi.org/10.1007/s11118-017-9638-6\">https://doi.org/10.1007/s11118-017-9638-6</a>","ieee":"M. Rösler, P. Graczyk, and T. Luks, “On the Green Function and Poisson Integrals of the Dunkl Laplacian,” <i>Potential Analysis</i>, vol. 48, no. 3, pp. 337–360, 2018, doi: <a href=\"https://doi.org/10.1007/s11118-017-9638-6\">10.1007/s11118-017-9638-6</a>.","chicago":"Rösler, Margit, Piotr Graczyk, and Tomasz Luks. “On the Green Function and Poisson Integrals of the Dunkl Laplacian.” <i>Potential Analysis</i> 48, no. 3 (2018): 337–60. <a href=\"https://doi.org/10.1007/s11118-017-9638-6\">https://doi.org/10.1007/s11118-017-9638-6</a>.","ama":"Rösler M, Graczyk P, Luks T. 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Integral representation and sharp asymptotic results for some Heckman-Opdam hypergeometric functions of type BC. <i>Transactions of the American Mathematical Society</i>, <i>368</i>(8), 6005–6032. <a href=\"https://doi.org/10.48550/ARXIV.1402.5793\">https://doi.org/10.48550/ARXIV.1402.5793</a>","short":"M. Rösler, M. Voit, Transactions of the American Mathematical Society 368 (2016) 6005–6032.","bibtex":"@article{Rösler_Voit_2016, title={Integral representation and sharp asymptotic results for some Heckman-Opdam hypergeometric functions of type BC}, volume={368}, DOI={<a href=\"https://doi.org/10.48550/ARXIV.1402.5793\">10.48550/ARXIV.1402.5793</a>}, number={8}, journal={Transactions of the American Mathematical Society}, publisher={ American Mathematical Society}, author={Rösler, Margit and Voit, Michael}, year={2016}, pages={6005–6032} }","mla":"Rösler, Margit, and Michael Voit. “Integral Representation and Sharp Asymptotic Results for Some Heckman-Opdam Hypergeometric Functions of Type BC.” <i>Transactions of the American Mathematical Society</i>, vol. 368, no. 8,  American Mathematical Society, 2016, pp. 6005–32, doi:<a href=\"https://doi.org/10.48550/ARXIV.1402.5793\">10.48550/ARXIV.1402.5793</a>.","chicago":"Rösler, Margit, and Michael Voit. “Integral Representation and Sharp Asymptotic Results for Some Heckman-Opdam Hypergeometric Functions of Type BC.” <i>Transactions of the American Mathematical Society</i> 368, no. 8 (2016): 6005–32. <a href=\"https://doi.org/10.48550/ARXIV.1402.5793\">https://doi.org/10.48550/ARXIV.1402.5793</a>.","ieee":"M. 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A multivariate version of the disk convolution. <i>Journal of Mathematical Analysis and Applications</i>, <i>435</i>(1), 701–717. <a href=\"https://doi.org/10.1016/j.jmaa.2015.10.062\">https://doi.org/10.1016/j.jmaa.2015.10.062</a>","ama":"Rösler M, Voit M. A multivariate version of the disk convolution. <i>Journal of Mathematical Analysis and Applications</i>. 2016;435(1):701-717. doi:<a href=\"https://doi.org/10.1016/j.jmaa.2015.10.062\">10.1016/j.jmaa.2015.10.062</a>","ieee":"M. Rösler and M. Voit, “A multivariate version of the disk convolution,” <i>Journal of Mathematical Analysis and Applications</i>, vol. 435, no. 1, pp. 701–717, 2016, doi: <a href=\"https://doi.org/10.1016/j.jmaa.2015.10.062\">10.1016/j.jmaa.2015.10.062</a>.","chicago":"Rösler, Margit, and Michael Voit. “A Multivariate Version of the Disk Convolution.” <i>Journal of Mathematical Analysis and Applications</i> 435, no. 1 (2016): 701–17. <a href=\"https://doi.org/10.1016/j.jmaa.2015.10.062\">https://doi.org/10.1016/j.jmaa.2015.10.062</a>."},"page":"701-717","intvolume":"       435","year":"2016","date_created":"2023-01-20T09:26:43Z","author":[{"first_name":"Margit","id":"37390","full_name":"Rösler, Margit","last_name":"Rösler"},{"full_name":"Voit, Michael","last_name":"Voit","first_name":"Michael"}],"volume":435,"date_updated":"2023-01-24T22:15:56Z","publisher":"Elsevier BV","doi":"10.1016/j.jmaa.2015.10.062","title":"A multivariate version of the disk convolution"},{"type":"journal_article","publication":"Symmetry, Integrability and Geometry: Methods and Applications","status":"public","_id":"38037","user_id":"93826","department":[{"_id":"555"}],"keyword":["Geometry and Topology","Mathematical Physics","Analysis"],"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["1815-0659"]},"issue":"013","year":"2015","citation":{"apa":"Rösler, M., &#38; Voit, M. (2015). A Central Limit Theorem for Random Walks on the Dual of a Compact Grassmannian. <i>Symmetry, Integrability and Geometry: Methods and Applications</i>, <i>11</i>(013), 18pp. <a href=\"https://doi.org/10.3842/sigma.2015.013\">https://doi.org/10.3842/sigma.2015.013</a>","short":"M. Rösler, M. Voit, Symmetry, Integrability and Geometry: Methods and Applications 11 (2015) 18pp.","bibtex":"@article{Rösler_Voit_2015, title={A Central Limit Theorem for Random Walks on the Dual of a Compact Grassmannian}, volume={11}, DOI={<a href=\"https://doi.org/10.3842/sigma.2015.013\">10.3842/sigma.2015.013</a>}, number={013}, journal={Symmetry, Integrability and Geometry: Methods and Applications}, publisher={SIGMA (Symmetry, Integrability and Geometry: Methods and Application)}, author={Rösler, Margit and Voit, Michael}, year={2015}, pages={18pp} }","mla":"Rösler, Margit, and Michael Voit. “A Central Limit Theorem for Random Walks on the Dual of a Compact Grassmannian.” <i>Symmetry, Integrability and Geometry: Methods and Applications</i>, vol. 11, no. 013, SIGMA (Symmetry, Integrability and Geometry: Methods and Application), 2015, p. 18pp, doi:<a href=\"https://doi.org/10.3842/sigma.2015.013\">10.3842/sigma.2015.013</a>.","ieee":"M. Rösler and M. Voit, “A Central Limit Theorem for Random Walks on the Dual of a Compact Grassmannian,” <i>Symmetry, Integrability and Geometry: Methods and Applications</i>, vol. 11, no. 013, p. 18pp, 2015, doi: <a href=\"https://doi.org/10.3842/sigma.2015.013\">10.3842/sigma.2015.013</a>.","chicago":"Rösler, Margit, and Michael Voit. “A Central Limit Theorem for Random Walks on the Dual of a Compact Grassmannian.” <i>Symmetry, Integrability and Geometry: Methods and Applications</i> 11, no. 013 (2015): 18pp. <a href=\"https://doi.org/10.3842/sigma.2015.013\">https://doi.org/10.3842/sigma.2015.013</a>.","ama":"Rösler M, Voit M. A Central Limit Theorem for Random Walks on the Dual of a Compact Grassmannian. <i>Symmetry, Integrability and Geometry: Methods and Applications</i>. 2015;11(013):18pp. doi:<a href=\"https://doi.org/10.3842/sigma.2015.013\">10.3842/sigma.2015.013</a>"},"page":"18pp","intvolume":"        11","publisher":"SIGMA (Symmetry, Integrability and Geometry: Methods and Application)","date_updated":"2023-01-24T22:15:37Z","author":[{"first_name":"Margit","full_name":"Rösler, Margit","id":"37390","last_name":"Rösler"},{"last_name":"Voit","full_name":"Voit, Michael","first_name":"Michael"}],"date_created":"2023-01-23T08:18:48Z","volume":11,"title":"A Central Limit Theorem for Random Walks on the Dual of a Compact Grassmannian","doi":"10.3842/sigma.2015.013"},{"citation":{"chicago":"Rösler, Margit, and Heiko Remling. “Convolution Algebras for Heckman–Opdam Polynomials Derived from Compact Grassmannians.” <i>Journal of Approximation Theory</i> 197 (2014): 30–48. <a href=\"https://doi.org/10.1016/j.jat.2014.07.005\">https://doi.org/10.1016/j.jat.2014.07.005</a>.","ieee":"M. Rösler and H. Remling, “Convolution algebras for Heckman–Opdam polynomials derived from compact Grassmannians,” <i>Journal of Approximation Theory</i>, vol. 197, pp. 30–48, 2014, doi: <a href=\"https://doi.org/10.1016/j.jat.2014.07.005\">10.1016/j.jat.2014.07.005</a>.","ama":"Rösler M, Remling H. Convolution algebras for Heckman–Opdam polynomials derived from compact Grassmannians. <i>Journal of Approximation Theory</i>. 2014;197:30-48. doi:<a href=\"https://doi.org/10.1016/j.jat.2014.07.005\">10.1016/j.jat.2014.07.005</a>","apa":"Rösler, M., &#38; Remling, H. (2014). Convolution algebras for Heckman–Opdam polynomials derived from compact Grassmannians. <i>Journal of Approximation Theory</i>, <i>197</i>, 30–48. <a href=\"https://doi.org/10.1016/j.jat.2014.07.005\">https://doi.org/10.1016/j.jat.2014.07.005</a>","mla":"Rösler, Margit, and Heiko Remling. “Convolution Algebras for Heckman–Opdam Polynomials Derived from Compact Grassmannians.” <i>Journal of Approximation Theory</i>, vol. 197, Elsevier BV, 2014, pp. 30–48, doi:<a href=\"https://doi.org/10.1016/j.jat.2014.07.005\">10.1016/j.jat.2014.07.005</a>.","short":"M. Rösler, H. Remling, Journal of Approximation Theory 197 (2014) 30–48.","bibtex":"@article{Rösler_Remling_2014, title={Convolution algebras for Heckman–Opdam polynomials derived from compact Grassmannians}, volume={197}, DOI={<a href=\"https://doi.org/10.1016/j.jat.2014.07.005\">10.1016/j.jat.2014.07.005</a>}, journal={Journal of Approximation Theory}, publisher={Elsevier BV}, author={Rösler, Margit and Remling, Heiko}, year={2014}, pages={30–48} }"},"intvolume":"       197","page":"30-48","year":"2014","publication_status":"published","publication_identifier":{"issn":["0021-9045"]},"doi":"10.1016/j.jat.2014.07.005","title":"Convolution algebras for Heckman–Opdam polynomials derived from compact Grassmannians","author":[{"last_name":"Rösler","full_name":"Rösler, Margit","id":"37390","first_name":"Margit"},{"first_name":"Heiko","full_name":"Remling, Heiko","last_name":"Remling"}],"date_created":"2023-01-20T09:30:22Z","volume":197,"publisher":"Elsevier BV","date_updated":"2023-01-24T22:15:33Z","status":"public","type":"journal_article","publication":"Journal of Approximation Theory","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","General Mathematics","Numerical Analysis","Analysis"],"user_id":"93826","department":[{"_id":"555"}],"_id":"37667"},{"issue":"8","publication_status":"published","publication_identifier":{"issn":["0010-437X","1570-5846"]},"citation":{"apa":"Rösler, M., Koornwinder, T., &#38; Voit, M. (2013). Limit transition between hypergeometric functions of type BC and type A. <i>Compositio Mathematica</i>, <i>149</i>(8), 1381–1400. <a href=\"https://doi.org/10.1112/s0010437x13007045\">https://doi.org/10.1112/s0010437x13007045</a>","bibtex":"@article{Rösler_Koornwinder_Voit_2013, title={Limit transition between hypergeometric functions of type BC and type A}, volume={149}, DOI={<a href=\"https://doi.org/10.1112/s0010437x13007045\">10.1112/s0010437x13007045</a>}, number={8}, journal={Compositio Mathematica}, publisher={Wiley}, author={Rösler, Margit and Koornwinder, Tom and Voit, Michael}, year={2013}, pages={1381–1400} }","mla":"Rösler, Margit, et al. “Limit Transition between Hypergeometric Functions of Type BC and Type A.” <i>Compositio Mathematica</i>, vol. 149, no. 8, Wiley, 2013, pp. 1381–400, doi:<a href=\"https://doi.org/10.1112/s0010437x13007045\">10.1112/s0010437x13007045</a>.","short":"M. Rösler, T. Koornwinder, M. Voit, Compositio Mathematica 149 (2013) 1381–1400.","ama":"Rösler M, Koornwinder T, Voit M. Limit transition between hypergeometric functions of type BC and type A. <i>Compositio Mathematica</i>. 2013;149(8):1381-1400. doi:<a href=\"https://doi.org/10.1112/s0010437x13007045\">10.1112/s0010437x13007045</a>","ieee":"M. Rösler, T. Koornwinder, and M. Voit, “Limit transition between hypergeometric functions of type BC and type A,” <i>Compositio Mathematica</i>, vol. 149, no. 8, pp. 1381–1400, 2013, doi: <a href=\"https://doi.org/10.1112/s0010437x13007045\">10.1112/s0010437x13007045</a>.","chicago":"Rösler, Margit, Tom Koornwinder, and Michael Voit. “Limit Transition between Hypergeometric Functions of Type BC and Type A.” <i>Compositio Mathematica</i> 149, no. 8 (2013): 1381–1400. <a href=\"https://doi.org/10.1112/s0010437x13007045\">https://doi.org/10.1112/s0010437x13007045</a>."},"intvolume":"       149","page":"1381-1400","year":"2013","date_created":"2023-01-20T09:37:16Z","author":[{"id":"37390","full_name":"Rösler, Margit","last_name":"Rösler","first_name":"Margit"},{"last_name":"Koornwinder","full_name":"Koornwinder, Tom","first_name":"Tom"},{"full_name":"Voit, Michael","last_name":"Voit","first_name":"Michael"}],"volume":149,"publisher":"Wiley","date_updated":"2023-01-24T22:15:13Z","doi":"10.1112/s0010437x13007045","title":"Limit transition between hypergeometric functions of type BC and type A","type":"journal_article","publication":"Compositio Mathematica","status":"public","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>Let <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0010437X13007045_inline1\" /><jats:tex-math>${F}_{BC} (\\lambda , k; t)$</jats:tex-math></jats:alternatives></jats:inline-formula> be the Heckman–Opdam hypergeometric function of type BC with multiplicities <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0010437X13007045_inline2\" /><jats:tex-math>$k= ({k}_{1} , {k}_{2} , {k}_{3} )$</jats:tex-math></jats:alternatives></jats:inline-formula> and weighted half-sum <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0010437X13007045_inline3\" /><jats:tex-math>$\\rho (k)$</jats:tex-math></jats:alternatives></jats:inline-formula> of positive roots. We prove that <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0010437X13007045_inline4\" /><jats:tex-math>${F}_{BC} (\\lambda + \\rho (k), k; t)$</jats:tex-math></jats:alternatives></jats:inline-formula> converges as <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0010437X13007045_inline5\" /><jats:tex-math>${k}_{1} + {k}_{2} \\rightarrow \\infty $</jats:tex-math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0010437X13007045_inline6\" /><jats:tex-math>${k}_{1} / {k}_{2} \\rightarrow \\infty $</jats:tex-math></jats:alternatives></jats:inline-formula> to a function of type A for <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0010437X13007045_inline7\" /><jats:tex-math>$t\\in { \\mathbb{R} }^{n} $</jats:tex-math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0010437X13007045_inline8\" /><jats:tex-math>$\\lambda \\in { \\mathbb{C} }^{n} $</jats:tex-math></jats:alternatives></jats:inline-formula>. This limit is obtained from a corresponding result for Jacobi polynomials of type BC, which is proven for a slightly more general limit behavior of the multiplicities, using an explicit representation of Jacobi polynomials in terms of Jack polynomials. Our limits include limit transitions for the spherical functions of non-compact Grassmann manifolds over one of the fields <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0010437X13007045_inline9\" /><jats:tex-math>$ \\mathbb{F} = \\mathbb{R} , \\mathbb{C} , \\mathbb{H} $</jats:tex-math></jats:alternatives></jats:inline-formula> when the rank is fixed and the dimension tends to infinity. The limit functions turn out to be exactly the spherical functions of the corresponding infinite-dimensional Grassmann manifold in the sense of Olshanski.</jats:p>","lang":"eng"}],"user_id":"93826","department":[{"_id":"555"}],"_id":"37672","language":[{"iso":"eng"}],"keyword":["Algebra and Number Theory"]},{"title":"Olshanski spherical functions for infinite dimensional motion groups of fixed rank","doi":"10.48550/ARXIV.1210.1351","publisher":"Heldermann ","date_updated":"2023-01-24T22:15:26Z","author":[{"first_name":"Margit","full_name":"Rösler, Margit","id":"37390","last_name":"Rösler"},{"first_name":"Michael","last_name":"Voit","full_name":"Voit, Michael"}],"date_created":"2023-01-23T08:26:17Z","year":"2013","citation":{"ieee":"M. Rösler and M. Voit, “Olshanski spherical functions for infinite dimensional motion groups of fixed rank,” <i>Journal of Lie Theory 23</i>, no. 4, pp. 899--920, 2013, doi: <a href=\"https://doi.org/10.48550/ARXIV.1210.1351\">10.48550/ARXIV.1210.1351</a>.","chicago":"Rösler, Margit, and Michael Voit. “Olshanski Spherical Functions for Infinite Dimensional Motion Groups of Fixed Rank.” <i>Journal of Lie Theory 23</i>, no. 4 (2013): 899--920. <a href=\"https://doi.org/10.48550/ARXIV.1210.1351\">https://doi.org/10.48550/ARXIV.1210.1351</a>.","ama":"Rösler M, Voit M. Olshanski spherical functions for infinite dimensional motion groups of fixed rank. <i>Journal of Lie Theory 23</i>. 2013;(4):899--920. doi:<a href=\"https://doi.org/10.48550/ARXIV.1210.1351\">10.48550/ARXIV.1210.1351</a>","mla":"Rösler, Margit, and Michael Voit. “Olshanski Spherical Functions for Infinite Dimensional Motion Groups of Fixed Rank.” <i>Journal of Lie Theory 23</i>, no. 4, Heldermann , 2013, pp. 899--920, doi:<a href=\"https://doi.org/10.48550/ARXIV.1210.1351\">10.48550/ARXIV.1210.1351</a>.","bibtex":"@article{Rösler_Voit_2013, title={Olshanski spherical functions for infinite dimensional motion groups of fixed rank}, DOI={<a href=\"https://doi.org/10.48550/ARXIV.1210.1351\">10.48550/ARXIV.1210.1351</a>}, number={4}, journal={Journal of Lie Theory 23}, publisher={Heldermann }, author={Rösler, Margit and Voit, Michael}, year={2013}, pages={899--920} }","short":"M. Rösler, M. Voit, Journal of Lie Theory 23 (2013) 899--920.","apa":"Rösler, M., &#38; Voit, M. (2013). Olshanski spherical functions for infinite dimensional motion groups of fixed rank. <i>Journal of Lie Theory 23</i>, <i>4</i>, 899--920. <a href=\"https://doi.org/10.48550/ARXIV.1210.1351\">https://doi.org/10.48550/ARXIV.1210.1351</a>"},"page":"899--920","publication_status":"published","issue":"4","language":[{"iso":"eng"}],"_id":"38038","user_id":"93826","department":[{"_id":"555"}],"status":"public","type":"journal_article","publication":"Journal of Lie Theory 23"},{"department":[{"_id":"555"}],"user_id":"93826","_id":"39911","extern":"1","language":[{"iso":"eng"}],"keyword":["General Mathematics"],"publication":"International Mathematics Research Notices","type":"journal_article","status":"public","date_created":"2023-01-25T09:26:07Z","author":[{"first_name":"Margit","last_name":"Rösler","full_name":"Rösler, Margit","id":"37390"},{"first_name":"H.","full_name":"Remling, H.","last_name":"Remling"}],"publisher":"Oxford University Press (OUP)","date_updated":"2023-01-26T17:50:05Z","doi":"10.1093/imrn/rnq239","title":"The Heat Semigroup in the Compact Heckman-Opdam Setting and the Segal-Bargmann Transform","issue":"18","publication_identifier":{"issn":["1073-7928","1687-0247"]},"publication_status":"published","page":"4200–4225","citation":{"ama":"Rösler M, Remling H. The Heat Semigroup in the Compact Heckman-Opdam Setting and the Segal-Bargmann Transform. <i>International Mathematics Research Notices</i>. 2011;(18):4200–4225. doi:<a href=\"https://doi.org/10.1093/imrn/rnq239\">10.1093/imrn/rnq239</a>","ieee":"M. Rösler and H. Remling, “The Heat Semigroup in the Compact Heckman-Opdam Setting and the Segal-Bargmann Transform,” <i>International Mathematics Research Notices</i>, no. 18, pp. 4200–4225, 2011, doi: <a href=\"https://doi.org/10.1093/imrn/rnq239\">10.1093/imrn/rnq239</a>.","chicago":"Rösler, Margit, and H. Remling. “The Heat Semigroup in the Compact Heckman-Opdam Setting and the Segal-Bargmann Transform.” <i>International Mathematics Research Notices</i>, no. 18 (2011): 4200–4225. <a href=\"https://doi.org/10.1093/imrn/rnq239\">https://doi.org/10.1093/imrn/rnq239</a>.","bibtex":"@article{Rösler_Remling_2011, title={The Heat Semigroup in the Compact Heckman-Opdam Setting and the Segal-Bargmann Transform}, DOI={<a href=\"https://doi.org/10.1093/imrn/rnq239\">10.1093/imrn/rnq239</a>}, number={18}, journal={International Mathematics Research Notices}, publisher={Oxford University Press (OUP)}, author={Rösler, Margit and Remling, H.}, year={2011}, pages={4200–4225} }","mla":"Rösler, Margit, and H. Remling. “The Heat Semigroup in the Compact Heckman-Opdam Setting and the Segal-Bargmann Transform.” <i>International Mathematics Research Notices</i>, no. 18, Oxford University Press (OUP), 2011, pp. 4200–4225, doi:<a href=\"https://doi.org/10.1093/imrn/rnq239\">10.1093/imrn/rnq239</a>.","short":"M. Rösler, H. Remling, International Mathematics Research Notices (2011) 4200–4225.","apa":"Rösler, M., &#38; Remling, H. (2011). The Heat Semigroup in the Compact Heckman-Opdam Setting and the Segal-Bargmann Transform. <i>International Mathematics Research Notices</i>, <i>18</i>, 4200–4225. <a href=\"https://doi.org/10.1093/imrn/rnq239\">https://doi.org/10.1093/imrn/rnq239</a>"},"year":"2011"},{"date_updated":"2023-01-26T17:50:51Z","author":[{"last_name":"Rösler","id":"37390","full_name":"Rösler, Margit","first_name":"Margit"},{"first_name":"Michael","last_name":"Voit","full_name":"Voit, Michael"}],"volume":284,"doi":"10.1002/mana.200710235","publication_status":"published","publication_identifier":{"issn":["0025-584X"]},"citation":{"chicago":"Rösler, Margit, and Michael Voit. “Limit Theorems for Radial Random Walks on p × Q-Matrices as p Tends to Infinity.” <i>Mathematische Nachrichten</i> 284, no. 1 (2011): 87–104. <a href=\"https://doi.org/10.1002/mana.200710235\">https://doi.org/10.1002/mana.200710235</a>.","ieee":"M. Rösler and M. Voit, “Limit theorems for radial random walks on p × q-matrices as p tends to infinity,” <i>Mathematische Nachrichten</i>, vol. 284, no. 1, pp. 87–104, 2011, doi: <a href=\"https://doi.org/10.1002/mana.200710235\">10.1002/mana.200710235</a>.","ama":"Rösler M, Voit M. Limit theorems for radial random walks on p × q-matrices as p tends to infinity. <i>Mathematische Nachrichten</i>. 2011;284(1):87-104. doi:<a href=\"https://doi.org/10.1002/mana.200710235\">10.1002/mana.200710235</a>","apa":"Rösler, M., &#38; Voit, M. (2011). Limit theorems for radial random walks on p × q-matrices as p tends to infinity. <i>Mathematische Nachrichten</i>, <i>284</i>(1), 87–104. <a href=\"https://doi.org/10.1002/mana.200710235\">https://doi.org/10.1002/mana.200710235</a>","mla":"Rösler, Margit, and Michael Voit. “Limit Theorems for Radial Random Walks on p × Q-Matrices as p Tends to Infinity.” <i>Mathematische Nachrichten</i>, vol. 284, no. 1, Wiley, 2011, pp. 87–104, doi:<a href=\"https://doi.org/10.1002/mana.200710235\">10.1002/mana.200710235</a>.","short":"M. Rösler, M. Voit, Mathematische Nachrichten 284 (2011) 87–104.","bibtex":"@article{Rösler_Voit_2011, title={Limit theorems for radial random walks on p × q-matrices as p tends to infinity}, volume={284}, DOI={<a href=\"https://doi.org/10.1002/mana.200710235\">10.1002/mana.200710235</a>}, number={1}, journal={Mathematische Nachrichten}, publisher={Wiley}, author={Rösler, Margit and Voit, Michael}, year={2011}, pages={87–104} }"},"intvolume":"       284","page":"87-104","_id":"39921","user_id":"93826","department":[{"_id":"555"}],"extern":"1","type":"journal_article","status":"public","publisher":"Wiley","date_created":"2023-01-25T09:30:21Z","title":"Limit theorems for radial random walks on p × q-matrices as p tends to infinity","issue":"1","year":"2011","keyword":["General Mathematics"],"language":[{"iso":"eng"}],"publication":"Mathematische Nachrichten"},{"year":"2010","citation":{"mla":"Rösler, Margit. “Positive Convolution Structure for a Class of Heckman–Opdam Hypergeometric Functions of Type BC.” <i>Journal of Functional Analysis</i>, vol. 258, no. 8, Elsevier BV, 2010, pp. 2779–800, doi:<a href=\"https://doi.org/10.1016/j.jfa.2009.12.007\">10.1016/j.jfa.2009.12.007</a>.","short":"M. Rösler, Journal of Functional Analysis 258 (2010) 2779–2800.","bibtex":"@article{Rösler_2010, title={Positive convolution structure for a class of Heckman–Opdam hypergeometric functions of type BC}, volume={258}, DOI={<a href=\"https://doi.org/10.1016/j.jfa.2009.12.007\">10.1016/j.jfa.2009.12.007</a>}, number={8}, journal={Journal of Functional Analysis}, publisher={Elsevier BV}, author={Rösler, Margit}, year={2010}, pages={2779–2800} }","apa":"Rösler, M. (2010). Positive convolution structure for a class of Heckman–Opdam hypergeometric functions of type BC. <i>Journal of Functional Analysis</i>, <i>258</i>(8), 2779–2800. <a href=\"https://doi.org/10.1016/j.jfa.2009.12.007\">https://doi.org/10.1016/j.jfa.2009.12.007</a>","chicago":"Rösler, Margit. “Positive Convolution Structure for a Class of Heckman–Opdam Hypergeometric Functions of Type BC.” <i>Journal of Functional Analysis</i> 258, no. 8 (2010): 2779–2800. <a href=\"https://doi.org/10.1016/j.jfa.2009.12.007\">https://doi.org/10.1016/j.jfa.2009.12.007</a>.","ieee":"M. Rösler, “Positive convolution structure for a class of Heckman–Opdam hypergeometric functions of type BC,” <i>Journal of Functional Analysis</i>, vol. 258, no. 8, pp. 2779–2800, 2010, doi: <a href=\"https://doi.org/10.1016/j.jfa.2009.12.007\">10.1016/j.jfa.2009.12.007</a>.","ama":"Rösler M. Positive convolution structure for a class of Heckman–Opdam hypergeometric functions of type BC. <i>Journal of Functional Analysis</i>. 2010;258(8):2779-2800. doi:<a href=\"https://doi.org/10.1016/j.jfa.2009.12.007\">10.1016/j.jfa.2009.12.007</a>"},"intvolume":"       258","page":"2779-2800","publication_status":"published","publication_identifier":{"issn":["0022-1236"]},"issue":"8","title":"Positive convolution structure for a class of Heckman–Opdam hypergeometric functions of type BC","doi":"10.1016/j.jfa.2009.12.007","date_updated":"2023-01-26T17:48:56Z","publisher":"Elsevier BV","date_created":"2023-01-25T09:32:04Z","author":[{"first_name":"Margit","last_name":"Rösler","id":"37390","full_name":"Rösler, Margit"}],"volume":258,"status":"public","type":"journal_article","publication":"Journal of Functional Analysis","keyword":["Analysis"],"extern":"1","language":[{"iso":"eng"}],"_id":"39924","user_id":"93826","department":[{"_id":"555"}]},{"extern":"1","language":[{"iso":"eng"}],"_id":"39950","department":[{"_id":"555"}],"user_id":"37390","status":"public","publication":"Infinite Dimensional Harmonic Analysis IV","type":"conference","title":"Convolution algebras for multivariable Bessel functions","doi":"10.1142/9789812832825_0017","date_updated":"2023-01-26T17:48:43Z","publisher":"World Scientific","date_created":"2023-01-25T10:01:16Z","author":[{"last_name":"Rösler","id":"37390","full_name":"Rösler, Margit","first_name":"Margit"}],"year":"2009","page":" 255–271","citation":{"mla":"Rösler, Margit. “Convolution Algebras for Multivariable Bessel Functions.” <i>Infinite Dimensional Harmonic Analysis IV</i>, World Scientific, 2009, pp. 255–271, doi:<a href=\"https://doi.org/10.1142/9789812832825_0017\">10.1142/9789812832825_0017</a>.","bibtex":"@inproceedings{Rösler_2009, title={Convolution algebras for multivariable Bessel functions}, DOI={<a href=\"https://doi.org/10.1142/9789812832825_0017\">10.1142/9789812832825_0017</a>}, booktitle={Infinite Dimensional Harmonic Analysis IV}, publisher={World Scientific}, author={Rösler, Margit}, year={2009}, pages={255–271} }","short":"M. Rösler, in: Infinite Dimensional Harmonic Analysis IV, World Scientific, 2009, pp. 255–271.","apa":"Rösler, M. (2009). Convolution algebras for multivariable Bessel functions. <i>Infinite Dimensional Harmonic Analysis IV</i>, 255–271. <a href=\"https://doi.org/10.1142/9789812832825_0017\">https://doi.org/10.1142/9789812832825_0017</a>","ama":"Rösler M. Convolution algebras for multivariable Bessel functions. In: <i>Infinite Dimensional Harmonic Analysis IV</i>. World Scientific; 2009:255–271. doi:<a href=\"https://doi.org/10.1142/9789812832825_0017\">10.1142/9789812832825_0017</a>","chicago":"Rösler, Margit. “Convolution Algebras for Multivariable Bessel Functions.” In <i>Infinite Dimensional Harmonic Analysis IV</i>, 255–271. World Scientific, 2009. <a href=\"https://doi.org/10.1142/9789812832825_0017\">https://doi.org/10.1142/9789812832825_0017</a>.","ieee":"M. Rösler, “Convolution algebras for multivariable Bessel functions,” in <i>Infinite Dimensional Harmonic Analysis IV</i>, 2009, pp. 255–271, doi: <a href=\"https://doi.org/10.1142/9789812832825_0017\">10.1142/9789812832825_0017</a>."},"publication_status":"published"}]