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On the Double Points of Operator Stable Lévy Processes. <i>Journal of Theoretical Probability</i>. 2017;30(1):297-325. doi:<a href=\"https://doi.org/10.1007/s10959-015-0638-4\">10.1007/s10959-015-0638-4</a>","bibtex":"@article{Luks_Xiao_2017, title={On the Double Points of Operator Stable Lévy Processes}, volume={30}, DOI={<a href=\"https://doi.org/10.1007/s10959-015-0638-4\">10.1007/s10959-015-0638-4</a>}, number={1}, journal={Journal of Theoretical Probability}, publisher={Springer Science and Business Media LLC}, author={Luks, Tomasz and Xiao, Yimin}, year={2017}, pages={297–325} }","mla":"Luks, Tomasz, and Yimin Xiao. “On the Double Points of Operator Stable Lévy Processes.” <i>Journal of Theoretical Probability</i>, vol. 30, no. 1, Springer Science and Business Media LLC, 2017, pp. 297–325, doi:<a href=\"https://doi.org/10.1007/s10959-015-0638-4\">10.1007/s10959-015-0638-4</a>."}},{"issue":"8","publication":"Transactions of the American Mathematical Society","type":"journal_article","department":[{"_id":"555"}],"date_created":"2023-01-23T08:09:20Z","publication_status":"published","date_updated":"2023-01-24T22:15:46Z","intvolume":"       368","title":"Integral representation and sharp asymptotic results for some Heckman-Opdam hypergeometric functions of type BC","year":"2016","author":[{"id":"37390","full_name":"Rösler, Margit","first_name":"Margit","last_name":"Rösler"},{"last_name":"Voit","first_name":"Michael","full_name":"Voit, Michael"}],"publication_identifier":{"issn":["1088-6850"]},"doi":"10.48550/ARXIV.1402.5793","language":[{"iso":"eng"}],"citation":{"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>.","short":"M. Rösler, M. Voit, Transactions of the American Mathematical Society 368 (2016) 6005–6032.","ieee":"M. Rösler and M. 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, pp. 6005–6032, 2016, doi: <a href=\"https://doi.org/10.48550/ARXIV.1402.5793\">10.48550/ARXIV.1402.5793</a>.","apa":"Rösler, M., &#38; Voit, M. (2016). 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>","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} }","ama":"Rösler M, Voit M. Integral representation and sharp asymptotic results for some Heckman-Opdam hypergeometric functions of type BC. <i>Transactions of the American Mathematical Society</i>. 2016;368(8):6005-6032. doi:<a href=\"https://doi.org/10.48550/ARXIV.1402.5793\">10.48550/ARXIV.1402.5793</a>","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>."},"status":"public","user_id":"37390","volume":368,"page":"6005-6032","publisher":" American Mathematical Society","_id":"38032"},{"doi":"10.1016/j.jmaa.2015.10.062","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2023-01-24T22:15:56Z","intvolume":"       435","year":"2016","title":"A multivariate version of the disk convolution","publication_identifier":{"issn":["0022-247X"]},"author":[{"id":"37390","first_name":"Margit","last_name":"Rösler","full_name":"Rösler, Margit"},{"last_name":"Voit","first_name":"Michael","full_name":"Voit, Michael"}],"keyword":["Applied Mathematics","Analysis"],"type":"journal_article","department":[{"_id":"555"}],"date_created":"2023-01-20T09:26:43Z","issue":"1","publication":"Journal of Mathematical Analysis and Applications","user_id":"37390","volume":435,"page":"701-717","publisher":"Elsevier BV","_id":"37663","status":"public","citation":{"mla":"Rösler, Margit, and Michael Voit. “A Multivariate Version of the Disk Convolution.” <i>Journal of Mathematical Analysis and Applications</i>, vol. 435, no. 1, Elsevier BV, 2016, pp. 701–17, doi:<a href=\"https://doi.org/10.1016/j.jmaa.2015.10.062\">10.1016/j.jmaa.2015.10.062</a>.","bibtex":"@article{Rösler_Voit_2016, title={A multivariate version of the disk convolution}, volume={435}, DOI={<a href=\"https://doi.org/10.1016/j.jmaa.2015.10.062\">10.1016/j.jmaa.2015.10.062</a>}, number={1}, journal={Journal of Mathematical Analysis and Applications}, publisher={Elsevier BV}, author={Rösler, Margit and Voit, Michael}, year={2016}, pages={701–717} }","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>.","apa":"Rösler, M., &#38; Voit, M. (2016). 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>","short":"M. Rösler, M. Voit, Journal of Mathematical Analysis and Applications 435 (2016) 701–717.","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>."}},{"citation":{"short":"R. Bañuelos, K. Bogdan, T. Luks, Journal of the London Mathematical Society 94 (2016) 462–478.","chicago":"Bañuelos, Rodrigo, Krzysztof Bogdan, and Tomasz Luks. “Hardy–Stein Identities and Square Functions for Semigroups.” <i>Journal of the London Mathematical Society</i> 94, no. 2 (2016): 462–78. <a href=\"https://doi.org/10.1112/jlms/jdw042\">https://doi.org/10.1112/jlms/jdw042</a>.","apa":"Bañuelos, R., Bogdan, K., &#38; Luks, T. (2016). Hardy–Stein identities and square functions for semigroups. <i>Journal of the London Mathematical Society</i>, <i>94</i>(2), 462–478. <a href=\"https://doi.org/10.1112/jlms/jdw042\">https://doi.org/10.1112/jlms/jdw042</a>","ieee":"R. Bañuelos, K. Bogdan, and T. Luks, “Hardy–Stein identities and square functions for semigroups,” <i>Journal of the London Mathematical Society</i>, vol. 94, no. 2, pp. 462–478, 2016, doi: <a href=\"https://doi.org/10.1112/jlms/jdw042\">10.1112/jlms/jdw042</a>.","ama":"Bañuelos R, Bogdan K, Luks T. Hardy–Stein identities and square functions for semigroups. <i>Journal of the London Mathematical Society</i>. 2016;94(2):462-478. doi:<a href=\"https://doi.org/10.1112/jlms/jdw042\">10.1112/jlms/jdw042</a>","bibtex":"@article{Bañuelos_Bogdan_Luks_2016, title={Hardy–Stein identities and square functions for semigroups}, volume={94}, DOI={<a href=\"https://doi.org/10.1112/jlms/jdw042\">10.1112/jlms/jdw042</a>}, number={2}, journal={Journal of the London Mathematical Society}, publisher={Wiley}, author={Bañuelos, Rodrigo and Bogdan, Krzysztof and Luks, Tomasz}, year={2016}, pages={462–478} }","mla":"Bañuelos, Rodrigo, et al. “Hardy–Stein Identities and Square Functions for Semigroups.” <i>Journal of the London Mathematical Society</i>, vol. 94, no. 2, Wiley, 2016, pp. 462–78, doi:<a href=\"https://doi.org/10.1112/jlms/jdw042\">10.1112/jlms/jdw042</a>."},"status":"public","user_id":"58312","volume":94,"page":"462-478","publisher":"Wiley","_id":"40066","extern":"1","publication":"Journal of the London Mathematical Society","issue":"2","keyword":["General Mathematics"],"type":"journal_article","department":[{"_id":"555"}],"date_created":"2023-01-25T15:43:14Z","date_updated":"2023-01-26T17:20:19Z","publication_status":"published","intvolume":"        94","year":"2016","title":"Hardy–Stein identities and square functions for semigroups","author":[{"first_name":"Rodrigo","last_name":"Bañuelos","full_name":"Bañuelos, Rodrigo"},{"full_name":"Bogdan, Krzysztof","last_name":"Bogdan","first_name":"Krzysztof"},{"full_name":"Luks, Tomasz","last_name":"Luks","first_name":"Tomasz","id":"58312"}],"publication_identifier":{"issn":["0024-6107","1469-7750"]},"doi":"10.1112/jlms/jdw042","language":[{"iso":"eng"}]},{"publication":"Symmetry, Integrability and Geometry: Methods and Applications","issue":"013","date_created":"2023-01-23T08:18:48Z","department":[{"_id":"555"}],"type":"journal_article","keyword":["Geometry and Topology","Mathematical Physics","Analysis"],"publication_identifier":{"issn":["1815-0659"]},"author":[{"id":"37390","full_name":"Rösler, Margit","last_name":"Rösler","first_name":"Margit"},{"full_name":"Voit, Michael","last_name":"Voit","first_name":"Michael"}],"title":"A Central Limit Theorem for Random Walks on the Dual of a Compact Grassmannian","year":"2015","intvolume":"        11","date_updated":"2023-01-24T22:15:37Z","publication_status":"published","language":[{"iso":"eng"}],"doi":"10.3842/sigma.2015.013","citation":{"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>.","short":"M. Rösler, M. Voit, Symmetry, Integrability and Geometry: Methods and Applications 11 (2015) 18pp.","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>","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>.","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>","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>."},"status":"public","_id":"38037","publisher":"SIGMA (Symmetry, Integrability and Geometry: Methods and Application)","page":"18pp","volume":11,"user_id":"93826"},{"citation":{"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>","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>.","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>.","short":"M. Rösler, H. Remling, Journal of Approximation Theory 197 (2014) 30–48.","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>.","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>","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} }"},"status":"public","volume":197,"user_id":"93826","_id":"37667","publisher":"Elsevier BV","page":"30-48","publication":"Journal of Approximation Theory","department":[{"_id":"555"}],"type":"journal_article","keyword":["Applied Mathematics","General Mathematics","Numerical Analysis","Analysis"],"date_created":"2023-01-20T09:30:22Z","intvolume":"       197","date_updated":"2023-01-24T22:15:33Z","publication_status":"published","author":[{"full_name":"Rösler, Margit","first_name":"Margit","last_name":"Rösler","id":"37390"},{"full_name":"Remling, Heiko","first_name":"Heiko","last_name":"Remling"}],"publication_identifier":{"issn":["0021-9045"]},"title":"Convolution algebras for Heckman–Opdam polynomials derived from compact Grassmannians","year":"2014","doi":"10.1016/j.jat.2014.07.005","language":[{"iso":"eng"}]},{"user_id":"58312","volume":44,"page":"193-215","_id":"40068","publisher":"Hiroshima University - Department of Mathematics","status":"public","citation":{"ama":"Bogdan K, Dyda B, Luks T. On Hardy spaces of local and nonlocal operators. <i>Hiroshima Mathematical Journal</i>. 2014;44(2):193-215. doi:<a href=\"https://doi.org/10.32917/hmj/1408972907\">10.32917/hmj/1408972907</a>","bibtex":"@article{Bogdan_Dyda_Luks_2014, title={On Hardy spaces of local and nonlocal operators}, volume={44}, DOI={<a href=\"https://doi.org/10.32917/hmj/1408972907\">10.32917/hmj/1408972907</a>}, number={2}, journal={Hiroshima Mathematical Journal}, publisher={Hiroshima University - Department of Mathematics}, author={Bogdan, Krzysztof and Dyda, Bartłomiej and Luks, Tomasz}, year={2014}, pages={193–215} }","mla":"Bogdan, Krzysztof, et al. “On Hardy Spaces of Local and Nonlocal Operators.” <i>Hiroshima Mathematical Journal</i>, vol. 44, no. 2, Hiroshima University - Department of Mathematics, 2014, pp. 193–215, doi:<a href=\"https://doi.org/10.32917/hmj/1408972907\">10.32917/hmj/1408972907</a>.","chicago":"Bogdan, Krzysztof, Bartłomiej Dyda, and Tomasz Luks. “On Hardy Spaces of Local and Nonlocal Operators.” <i>Hiroshima Mathematical Journal</i> 44, no. 2 (2014): 193–215. <a href=\"https://doi.org/10.32917/hmj/1408972907\">https://doi.org/10.32917/hmj/1408972907</a>.","short":"K. Bogdan, B. Dyda, T. Luks, Hiroshima Mathematical Journal 44 (2014) 193–215.","apa":"Bogdan, K., Dyda, B., &#38; Luks, T. (2014). On Hardy spaces of local and nonlocal operators. <i>Hiroshima Mathematical Journal</i>, <i>44</i>(2), 193–215. <a href=\"https://doi.org/10.32917/hmj/1408972907\">https://doi.org/10.32917/hmj/1408972907</a>","ieee":"K. Bogdan, B. Dyda, and T. Luks, “On Hardy spaces of local and nonlocal operators,” <i>Hiroshima Mathematical Journal</i>, vol. 44, no. 2, pp. 193–215, 2014, doi: <a href=\"https://doi.org/10.32917/hmj/1408972907\">10.32917/hmj/1408972907</a>."},"doi":"10.32917/hmj/1408972907","language":[{"iso":"eng"}],"date_updated":"2023-01-26T17:20:41Z","publication_status":"published","intvolume":"        44","title":"On Hardy spaces of local and nonlocal operators","year":"2014","publication_identifier":{"issn":["0018-2079"]},"author":[{"last_name":"Bogdan","first_name":"Krzysztof","full_name":"Bogdan, Krzysztof"},{"first_name":"Bartłomiej","last_name":"Dyda","full_name":"Dyda, Bartłomiej"},{"first_name":"Tomasz","last_name":"Luks","full_name":"Luks, Tomasz","id":"58312"}],"type":"journal_article","department":[{"_id":"555"}],"date_created":"2023-01-25T15:46:01Z","extern":"1","issue":"2","publication":"Hiroshima Mathematical Journal"},{"doi":"10.1112/s0010437x13007045","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2023-01-24T22:15:13Z","intvolume":"       149","year":"2013","title":"Limit transition between hypergeometric functions of type BC and type A","author":[{"id":"37390","last_name":"Rösler","first_name":"Margit","full_name":"Rösler, Margit"},{"full_name":"Koornwinder, Tom","last_name":"Koornwinder","first_name":"Tom"},{"first_name":"Michael","last_name":"Voit","full_name":"Voit, Michael"}],"publication_identifier":{"issn":["0010-437X","1570-5846"]},"type":"journal_article","keyword":["Algebra and Number Theory"],"department":[{"_id":"555"}],"date_created":"2023-01-20T09:37:16Z","abstract":[{"lang":"eng","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>"}],"publication":"Compositio Mathematica","issue":"8","user_id":"93826","volume":149,"page":"1381-1400","publisher":"Wiley","_id":"37672","status":"public","citation":{"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>","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>.","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>.","short":"M. Rösler, T. Koornwinder, M. Voit, Compositio Mathematica 149 (2013) 1381–1400.","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>","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>."}},{"department":[{"_id":"555"}],"type":"journal_article","date_created":"2023-01-23T08:26:17Z","citation":{"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} }","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>.","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>.","short":"M. Rösler, M. Voit, Journal of Lie Theory 23 (2013) 899--920.","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>.","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>"},"publication":"Journal of Lie Theory 23","issue":"4","doi":"10.48550/ARXIV.1210.1351","user_id":"93826","_id":"38038","publisher":"Heldermann ","language":[{"iso":"eng"}],"page":"899--920","date_updated":"2023-01-24T22:15:26Z","publication_status":"published","author":[{"last_name":"Rösler","first_name":"Margit","full_name":"Rösler, Margit","id":"37390"},{"first_name":"Michael","last_name":"Voit","full_name":"Voit, Michael"}],"status":"public","year":"2013","title":"Olshanski spherical functions for infinite dimensional motion groups of fixed rank"},{"status":"public","page":"29-67","_id":"40072","publisher":"Springer Science and Business Media LLC","user_id":"58312","volume":39,"citation":{"short":"T. Luks, Potential Analysis 39 (2013) 29–67.","chicago":"Luks, Tomasz. “Boundary Behavior of α-Harmonic Functions on the Complement of the Sphere and Hyperplane.” <i>Potential Analysis</i> 39, no. 1 (2013): 29–67. <a href=\"https://doi.org/10.1007/s11118-012-9321-x\">https://doi.org/10.1007/s11118-012-9321-x</a>.","ieee":"T. Luks, “Boundary Behavior of α-Harmonic Functions on the Complement of the Sphere and Hyperplane,” <i>Potential Analysis</i>, vol. 39, no. 1, pp. 29–67, 2013, doi: <a href=\"https://doi.org/10.1007/s11118-012-9321-x\">10.1007/s11118-012-9321-x</a>.","apa":"Luks, T. (2013). Boundary Behavior of α-Harmonic Functions on the Complement of the Sphere and Hyperplane. <i>Potential Analysis</i>, <i>39</i>(1), 29–67. <a href=\"https://doi.org/10.1007/s11118-012-9321-x\">https://doi.org/10.1007/s11118-012-9321-x</a>","bibtex":"@article{Luks_2013, title={Boundary Behavior of α-Harmonic Functions on the Complement of the Sphere and Hyperplane}, volume={39}, DOI={<a href=\"https://doi.org/10.1007/s11118-012-9321-x\">10.1007/s11118-012-9321-x</a>}, number={1}, journal={Potential Analysis}, publisher={Springer Science and Business Media LLC}, author={Luks, Tomasz}, year={2013}, pages={29–67} }","ama":"Luks T. Boundary Behavior of α-Harmonic Functions on the Complement of the Sphere and Hyperplane. <i>Potential Analysis</i>. 2013;39(1):29-67. doi:<a href=\"https://doi.org/10.1007/s11118-012-9321-x\">10.1007/s11118-012-9321-x</a>","mla":"Luks, Tomasz. “Boundary Behavior of α-Harmonic Functions on the Complement of the Sphere and Hyperplane.” <i>Potential Analysis</i>, vol. 39, no. 1, Springer Science and Business Media LLC, 2013, pp. 29–67, doi:<a href=\"https://doi.org/10.1007/s11118-012-9321-x\">10.1007/s11118-012-9321-x</a>."},"title":"Boundary Behavior of α-Harmonic Functions on the Complement of the Sphere and Hyperplane","year":"2013","author":[{"full_name":"Luks, Tomasz","last_name":"Luks","first_name":"Tomasz","id":"58312"}],"publication_identifier":{"issn":["0926-2601","1572-929X"]},"publication_status":"published","date_updated":"2023-01-26T17:29:16Z","intvolume":"        39","language":[{"iso":"eng"}],"doi":"10.1007/s11118-012-9321-x","publication":"Potential Analysis","issue":"1","extern":"1","date_created":"2023-01-25T15:50:45Z","type":"journal_article","department":[{"_id":"555"}]},{"citation":{"mla":"Graczyk, Piotr, et al. “Martin Representation and Relative Fatou Theorem for Fractional Laplacian with a Gradient Perturbation.” <i>Positivity</i>, vol. 17, no. 4, Springer Science and Business Media LLC, 2013, pp. 1043–70, doi:<a href=\"https://doi.org/10.1007/s11117-012-0220-6\">10.1007/s11117-012-0220-6</a>.","bibtex":"@article{Graczyk_Jakubowski_Luks_2013, title={Martin representation and Relative Fatou Theorem for fractional Laplacian with a gradient perturbation}, volume={17}, DOI={<a href=\"https://doi.org/10.1007/s11117-012-0220-6\">10.1007/s11117-012-0220-6</a>}, number={4}, journal={Positivity}, publisher={Springer Science and Business Media LLC}, author={Graczyk, Piotr and Jakubowski, Tomasz and Luks, Tomasz}, year={2013}, pages={1043–1070} }","ama":"Graczyk P, Jakubowski T, Luks T. Martin representation and Relative Fatou Theorem for fractional Laplacian with a gradient perturbation. <i>Positivity</i>. 2013;17(4):1043-1070. doi:<a href=\"https://doi.org/10.1007/s11117-012-0220-6\">10.1007/s11117-012-0220-6</a>","ieee":"P. Graczyk, T. Jakubowski, and T. Luks, “Martin representation and Relative Fatou Theorem for fractional Laplacian with a gradient perturbation,” <i>Positivity</i>, vol. 17, no. 4, pp. 1043–1070, 2013, doi: <a href=\"https://doi.org/10.1007/s11117-012-0220-6\">10.1007/s11117-012-0220-6</a>.","apa":"Graczyk, P., Jakubowski, T., &#38; Luks, T. (2013). Martin representation and Relative Fatou Theorem for fractional Laplacian with a gradient perturbation. <i>Positivity</i>, <i>17</i>(4), 1043–1070. <a href=\"https://doi.org/10.1007/s11117-012-0220-6\">https://doi.org/10.1007/s11117-012-0220-6</a>","chicago":"Graczyk, Piotr, Tomasz Jakubowski, and Tomasz Luks. “Martin Representation and Relative Fatou Theorem for Fractional Laplacian with a Gradient Perturbation.” <i>Positivity</i> 17, no. 4 (2013): 1043–70. <a href=\"https://doi.org/10.1007/s11117-012-0220-6\">https://doi.org/10.1007/s11117-012-0220-6</a>.","short":"P. Graczyk, T. Jakubowski, T. Luks, Positivity 17 (2013) 1043–1070."},"status":"public","_id":"40070","publisher":"Springer Science and Business Media LLC","page":"1043-1070","volume":17,"user_id":"58312","issue":"4","publication":"Positivity","extern":"1","date_created":"2023-01-25T15:49:25Z","department":[{"_id":"555"}],"type":"journal_article","author":[{"full_name":"Graczyk, Piotr","first_name":"Piotr","last_name":"Graczyk"},{"full_name":"Jakubowski, Tomasz","last_name":"Jakubowski","first_name":"Tomasz"},{"last_name":"Luks","first_name":"Tomasz","full_name":"Luks, Tomasz","id":"58312"}],"publication_identifier":{"issn":["1385-1292","1572-9281"]},"title":"Martin representation and Relative Fatou Theorem for fractional Laplacian with a gradient perturbation","year":"2013","intvolume":"        17","date_updated":"2023-01-26T17:21:01Z","publication_status":"published","language":[{"iso":"eng"}],"doi":"10.1007/s11117-012-0220-6"},{"title":"Hardy spaces for the Laplacian with lower order perturbations","year":"2011","publication_identifier":{"issn":["0039-3223","1730-6337"]},"author":[{"id":"58312","full_name":"Luks, Tomasz","first_name":"Tomasz","last_name":"Luks"}],"publication_status":"published","date_updated":"2023-01-26T17:21:25Z","intvolume":"       204","language":[{"iso":"eng"}],"doi":"10.4064/sm204-1-3","publication":"Studia Mathematica","issue":"1","extern":"1","date_created":"2023-01-25T15:52:13Z","type":"journal_article","department":[{"_id":"555"}],"status":"public","page":"39-62","publisher":"Institute of Mathematics, Polish Academy of Sciences","_id":"40073","user_id":"58312","volume":204,"citation":{"apa":"Luks, T. (2011). Hardy spaces for the Laplacian with lower order perturbations. <i>Studia Mathematica</i>, <i>204</i>(1), 39–62. <a href=\"https://doi.org/10.4064/sm204-1-3\">https://doi.org/10.4064/sm204-1-3</a>","ieee":"T. Luks, “Hardy spaces for the Laplacian with lower order perturbations,” <i>Studia Mathematica</i>, vol. 204, no. 1, pp. 39–62, 2011, doi: <a href=\"https://doi.org/10.4064/sm204-1-3\">10.4064/sm204-1-3</a>.","chicago":"Luks, Tomasz. “Hardy Spaces for the Laplacian with Lower Order Perturbations.” <i>Studia Mathematica</i> 204, no. 1 (2011): 39–62. <a href=\"https://doi.org/10.4064/sm204-1-3\">https://doi.org/10.4064/sm204-1-3</a>.","short":"T. Luks, Studia Mathematica 204 (2011) 39–62.","mla":"Luks, Tomasz. “Hardy Spaces for the Laplacian with Lower Order Perturbations.” <i>Studia Mathematica</i>, vol. 204, no. 1, Institute of Mathematics, Polish Academy of Sciences, 2011, pp. 39–62, doi:<a href=\"https://doi.org/10.4064/sm204-1-3\">10.4064/sm204-1-3</a>.","ama":"Luks T. Hardy spaces for the Laplacian with lower order perturbations. <i>Studia Mathematica</i>. 2011;204(1):39-62. doi:<a href=\"https://doi.org/10.4064/sm204-1-3\">10.4064/sm204-1-3</a>","bibtex":"@article{Luks_2011, title={Hardy spaces for the Laplacian with lower order perturbations}, volume={204}, DOI={<a href=\"https://doi.org/10.4064/sm204-1-3\">10.4064/sm204-1-3</a>}, number={1}, journal={Studia Mathematica}, publisher={Institute of Mathematics, Polish Academy of Sciences}, author={Luks, Tomasz}, year={2011}, pages={39–62} }"}}]