[{"publication_status":"epub_ahead","year":"2024","citation":{"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>.","short":"D. Brennecken, M. Rösler, Indagationes Mathematicae (2024).","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} }","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>","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>.","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>."},"date_updated":"2024-07-15T09:09:55Z","publisher":"Elsevier","date_created":"2024-06-19T08:46:08Z","author":[{"id":"55911","full_name":"Brennecken, Dominik","last_name":"Brennecken","first_name":"Dominik"},{"last_name":"Rösler","full_name":"Rösler, Margit","id":"37390","first_name":"Margit"}],"title":"Limits of Bessel functions for root systems as the rank tends to  infinity","doi":"10.1016/j.indag.2024.05.004","publication":"Indagationes Mathematicae","type":"journal_article","abstract":[{"lang":"eng","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."}],"status":"public","_id":"54820","user_id":"82981","language":[{"iso":"eng"}]},{"author":[{"id":"55911","full_name":"Brennecken, Dominik","last_name":"Brennecken","first_name":"Dominik"}],"date_created":"2024-04-05T13:55:33Z","volume":535,"publisher":"Elsevier BV","date_updated":"2024-09-03T14:40:46Z","doi":"10.1016/j.jmaa.2024.128125","title":"Hankel transform, K-Bessel functions and zeta distributions in the Dunkl setting","issue":"2","publication_status":"published","publication_identifier":{"issn":["0022-247X"]},"citation":{"chicago":"Brennecken, Dominik. “Hankel Transform, K-Bessel Functions and Zeta Distributions in the Dunkl Setting.” <i>Journal of Mathematical Analysis and Applications</i> 535, no. 2 (2024). <a href=\"https://doi.org/10.1016/j.jmaa.2024.128125\">https://doi.org/10.1016/j.jmaa.2024.128125</a>.","ieee":"D. Brennecken, “Hankel transform, K-Bessel functions and zeta distributions in the Dunkl setting,” <i>Journal of Mathematical Analysis and Applications</i>, vol. 535, no. 2, Art. no. 128125, 2024, doi: <a href=\"https://doi.org/10.1016/j.jmaa.2024.128125\">10.1016/j.jmaa.2024.128125</a>.","ama":"Brennecken D. Hankel transform, K-Bessel functions and zeta distributions in the Dunkl setting. <i>Journal of Mathematical Analysis and Applications</i>. 2024;535(2). doi:<a href=\"https://doi.org/10.1016/j.jmaa.2024.128125\">10.1016/j.jmaa.2024.128125</a>","apa":"Brennecken, D. (2024). Hankel transform, K-Bessel functions and zeta distributions in the Dunkl setting. <i>Journal of Mathematical Analysis and Applications</i>, <i>535</i>(2), Article 128125. <a href=\"https://doi.org/10.1016/j.jmaa.2024.128125\">https://doi.org/10.1016/j.jmaa.2024.128125</a>","short":"D. Brennecken, Journal of Mathematical Analysis and Applications 535 (2024).","bibtex":"@article{Brennecken_2024, title={Hankel transform, K-Bessel functions and zeta distributions in the Dunkl setting}, volume={535}, DOI={<a href=\"https://doi.org/10.1016/j.jmaa.2024.128125\">10.1016/j.jmaa.2024.128125</a>}, number={2128125}, journal={Journal of Mathematical Analysis and Applications}, publisher={Elsevier BV}, author={Brennecken, Dominik}, year={2024} }","mla":"Brennecken, Dominik. “Hankel Transform, K-Bessel Functions and Zeta Distributions in the Dunkl Setting.” <i>Journal of Mathematical Analysis and Applications</i>, vol. 535, no. 2, 128125, Elsevier BV, 2024, doi:<a href=\"https://doi.org/10.1016/j.jmaa.2024.128125\">10.1016/j.jmaa.2024.128125</a>."},"intvolume":"       535","year":"2024","user_id":"55911","department":[{"_id":"555"}],"_id":"53300","language":[{"iso":"eng"}],"article_number":"128125","keyword":["Applied Mathematics","Analysis"],"type":"journal_article","publication":"Journal of Mathematical Analysis and Applications","status":"public"},{"publication_identifier":{"isbn":["978-3-031-57004-9"]},"publication_status":"published","year":"2024","intvolume":"         5","page":"425","citation":{"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.","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.","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.","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} }","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.","short":"D. Brennecken, M. Rösler, in: M. Chatzakou, M. Ruzhansky, D. Stoeva (Eds.), Women in Analysis and PDE, Birkhäuser Cham, 2024, p. 425."},"date_updated":"2024-09-05T06:58:54Z","publisher":"Birkhäuser Cham","volume":5,"author":[{"id":"55911","full_name":"Brennecken, Dominik","last_name":"Brennecken","first_name":"Dominik"},{"first_name":"Margit","last_name":"Rösler","id":"37390","full_name":"Rösler, Margit"}],"date_created":"2024-09-03T15:31:27Z","title":"The Laplace transform in Dunkl theory","publication":"Women in Analysis and PDE","type":"book_chapter","editor":[{"first_name":"Marianna","full_name":"Chatzakou, Marianna","last_name":"Chatzakou"},{"last_name":"Ruzhansky","full_name":"Ruzhansky, Michael","first_name":"Michael"},{"first_name":"Diana","last_name":"Stoeva","full_name":"Stoeva, Diana"}],"status":"public","_id":"56001","department":[{"_id":"555"}],"series_title":"Trends in Mathematics: Research Perspectives Ghent Analysis and PDE Cente","user_id":"82981","language":[{"iso":"eng"}]},{"author":[{"last_name":"Brennecken","id":"55911","full_name":"Brennecken, Dominik","first_name":"Dominik"}],"date_created":"2024-10-07T11:44:00Z","publisher":"Wiley","date_updated":"2024-10-07T11:46:15Z","doi":"10.1002/mana.202300370","title":"Dunkl convolution and elliptic regularity for Dunkl operators","publication_status":"published","publication_identifier":{"issn":["0025-584X","1522-2616"]},"citation":{"chicago":"Brennecken, Dominik. “Dunkl Convolution and Elliptic Regularity for Dunkl Operators.” <i>Mathematische Nachrichten</i>, 2024. <a href=\"https://doi.org/10.1002/mana.202300370\">https://doi.org/10.1002/mana.202300370</a>.","ieee":"D. Brennecken, “Dunkl convolution and elliptic regularity for Dunkl operators,” <i>Mathematische Nachrichten</i>, 2024, doi: <a href=\"https://doi.org/10.1002/mana.202300370\">10.1002/mana.202300370</a>.","ama":"Brennecken D. Dunkl convolution and elliptic regularity for Dunkl operators. <i>Mathematische Nachrichten</i>. Published online 2024. doi:<a href=\"https://doi.org/10.1002/mana.202300370\">10.1002/mana.202300370</a>","short":"D. Brennecken, Mathematische Nachrichten (2024).","bibtex":"@article{Brennecken_2024, title={Dunkl convolution and elliptic regularity for Dunkl operators}, DOI={<a href=\"https://doi.org/10.1002/mana.202300370\">10.1002/mana.202300370</a>}, journal={Mathematische Nachrichten}, publisher={Wiley}, author={Brennecken, Dominik}, year={2024} }","mla":"Brennecken, Dominik. “Dunkl Convolution and Elliptic Regularity for Dunkl Operators.” <i>Mathematische Nachrichten</i>, Wiley, 2024, doi:<a href=\"https://doi.org/10.1002/mana.202300370\">10.1002/mana.202300370</a>.","apa":"Brennecken, D. (2024). Dunkl convolution and elliptic regularity for Dunkl operators. <i>Mathematische Nachrichten</i>. <a href=\"https://doi.org/10.1002/mana.202300370\">https://doi.org/10.1002/mana.202300370</a>"},"year":"2024","user_id":"55911","department":[{"_id":"555"}],"_id":"56366","language":[{"iso":"eng"}],"type":"journal_article","publication":"Mathematische Nachrichten","status":"public","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>We discuss in which cases the Dunkl convolution  of distributions , possibly both with non‐compact support, can be defined and study its analytic properties. We prove results on the (singular‐)support of Dunkl convolutions. Based on this, we are able to prove a theorem on elliptic regularity for a certain class of Dunkl operators, called elliptic Dunkl operators. Finally, for the root system  we consider the Riesz distributions  and prove that their Dunkl convolution exists and that  holds.</jats:p>"}]},{"issue":"4","publication_status":"published","citation":{"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>","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.","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>.","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>.","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>"},"intvolume":"       376","page":"2419-2447","year":"2023","date_created":"2023-01-12T08:32:44Z","author":[{"id":"55911","full_name":"Brennecken, Dominik","last_name":"Brennecken","first_name":"Dominik"},{"first_name":"Margit","last_name":"Rösler","id":"37390","full_name":"Rösler, Margit"}],"volume":376,"publisher":" American Mathematical Society","date_updated":"2024-04-24T12:47:49Z","doi":"10.1090/tran/8860","title":"The Dunkl-Laplace transform and Macdonald’s hypergeometric series","type":"journal_article","publication":"Transactions of the American Mathematical Society","status":"public","user_id":"37390","department":[{"_id":"555"}],"_id":"36294","language":[{"iso":"eng"}]},{"date_updated":"2024-02-19T06:27:09Z","publisher":"Heldermann Verlag","author":[{"first_name":"Dominik","last_name":"Brennecken","full_name":"Brennecken, Dominik","id":"55911"},{"id":"220","full_name":"Hilgert, Joachim","last_name":"Hilgert","first_name":"Joachim"},{"full_name":"Ciardo, Lorenzo","last_name":"Ciardo","first_name":"Lorenzo"}],"date_created":"2023-01-12T08:23:28Z","volume":31,"title":"Algebraically Independent Generators for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R)","doi":"10.48550/arXiv.2008.07479","publication_status":"published","issue":"2","year":"2021","citation":{"apa":"Brennecken, D., Hilgert, J., &#38; Ciardo, L. (2021). Algebraically Independent Generators for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R). <i>Journal of Lie Theory</i>, <i>31</i>(2), 459--468. <a href=\"https://doi.org/10.48550/arXiv.2008.07479\">https://doi.org/10.48550/arXiv.2008.07479</a>","short":"D. Brennecken, J. Hilgert, L. Ciardo, Journal of Lie Theory 31 (2021) 459--468.","bibtex":"@article{Brennecken_Hilgert_Ciardo_2021, title={Algebraically Independent Generators for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R)}, volume={31}, DOI={<a href=\"https://doi.org/10.48550/arXiv.2008.07479\">10.48550/arXiv.2008.07479</a>}, number={2}, journal={Journal of Lie Theory}, publisher={Heldermann Verlag}, author={Brennecken, Dominik and Hilgert, Joachim and Ciardo, Lorenzo}, year={2021}, pages={459--468} }","mla":"Brennecken, Dominik, et al. “Algebraically Independent Generators for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R).” <i>Journal of Lie Theory</i>, vol. 31, no. 2, Heldermann Verlag, 2021, pp. 459--468, doi:<a href=\"https://doi.org/10.48550/arXiv.2008.07479\">10.48550/arXiv.2008.07479</a>.","ama":"Brennecken D, Hilgert J, Ciardo L. Algebraically Independent Generators for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R). <i>Journal of Lie Theory</i>. 2021;31(2):459--468. doi:<a href=\"https://doi.org/10.48550/arXiv.2008.07479\">10.48550/arXiv.2008.07479</a>","chicago":"Brennecken, Dominik, Joachim Hilgert, and Lorenzo Ciardo. “Algebraically Independent Generators for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R).” <i>Journal of Lie Theory</i> 31, no. 2 (2021): 459--468. <a href=\"https://doi.org/10.48550/arXiv.2008.07479\">https://doi.org/10.48550/arXiv.2008.07479</a>.","ieee":"D. Brennecken, J. Hilgert, and L. Ciardo, “Algebraically Independent Generators for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R),” <i>Journal of Lie Theory</i>, vol. 31, no. 2, pp. 459--468, 2021, doi: <a href=\"https://doi.org/10.48550/arXiv.2008.07479\">10.48550/arXiv.2008.07479</a>."},"intvolume":"        31","page":"459--468","_id":"36271","user_id":"49063","department":[{"_id":"555"},{"_id":"91"}],"language":[{"iso":"eng"}],"type":"journal_article","publication":"Journal of Lie Theory","status":"public"}]