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Birth and H. Glöckner, “Continuity of convolution of test functions on Lie groups,” <i>Canadian Journal of Mathematics</i>, vol. 66, no. 1, pp. 102–140, 2014, doi: <a href=\"https://doi.org/10.4153/CJM-2012-035-6\">10.4153/CJM-2012-035-6</a>.","short":"L. Birth, H. Glöckner, Canadian Journal of Mathematics 66 (2014) 102–140.","bibtex":"@article{Birth_Glöckner_2014, title={Continuity of convolution of test functions on Lie groups}, volume={66}, DOI={<a href=\"https://doi.org/10.4153/CJM-2012-035-6\">10.4153/CJM-2012-035-6</a>}, number={1}, journal={Canadian Journal of Mathematics}, author={Birth, Lidia and Glöckner, Helge}, year={2014}, pages={102–140} }","mla":"Birth, Lidia, and Helge Glöckner. “Continuity of Convolution of Test Functions on Lie Groups.” <i>Canadian Journal of Mathematics</i>, vol. 66, no. 1, 2014, pp. 102–140, doi:<a href=\"https://doi.org/10.4153/CJM-2012-035-6\">10.4153/CJM-2012-035-6</a>.","ama":"Birth L, Glöckner H. Continuity of convolution of test functions on Lie groups. <i>Canadian Journal of Mathematics</i>. 2014;66(1):102–140. doi:<a href=\"https://doi.org/10.4153/CJM-2012-035-6\">10.4153/CJM-2012-035-6</a>","apa":"Birth, L., &#38; Glöckner, H. (2014). Continuity of convolution of test functions on Lie groups. <i>Canadian Journal of Mathematics</i>, <i>66</i>(1), 102–140. <a href=\"https://doi.org/10.4153/CJM-2012-035-6\">https://doi.org/10.4153/CJM-2012-035-6</a>"},"page":"102–140","intvolume":"        66","year":"2014","issue":"1","publication_identifier":{"issn":["0008-414X"]},"quality_controlled":"1","doi":"10.4153/CJM-2012-035-6","title":"Continuity of convolution of test functions on Lie groups","author":[{"full_name":"Birth, Lidia","last_name":"Birth","first_name":"Lidia"},{"id":"178","full_name":"Glöckner, Helge","last_name":"Glöckner","first_name":"Helge"}],"date_created":"2026-02-26T10:57:07Z","volume":66,"date_updated":"2026-02-27T08:28:36Z"},{"_id":"64666","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"user_id":"178","article_type":"original","type":"journal_article","status":"public","date_updated":"2026-02-27T08:29:40Z","volume":366,"author":[{"id":"178","full_name":"Glöckner, Helge","last_name":"Glöckner","first_name":"Helge"},{"first_name":"Lutz G.","full_name":"Lucht, Lutz G.","last_name":"Lucht"}],"doi":"10.1090/S0002-9947-2013-06018-7","publication_identifier":{"issn":["0002-9947"]},"intvolume":"       366","page":"3275–3293","citation":{"chicago":"Glöckner, Helge, and Lutz G. 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Lucht, Transactions of the American Mathematical Society 366 (2014) 3275–3293.","mla":"Glöckner, Helge, and Lutz G. Lucht. “Weighted Inversion of General Dirichlet Series.” <i>Transactions of the American Mathematical Society</i>, vol. 366, no. 6, 2014, pp. 3275–3293, doi:<a href=\"https://doi.org/10.1090/S0002-9947-2013-06018-7\">10.1090/S0002-9947-2013-06018-7</a>.","apa":"Glöckner, H., &#38; Lucht, L. G. (2014). Weighted inversion of general Dirichlet series. <i>Transactions of the American Mathematical Society</i>, <i>366</i>(6), 3275–3293. <a href=\"https://doi.org/10.1090/S0002-9947-2013-06018-7\">https://doi.org/10.1090/S0002-9947-2013-06018-7</a>","ama":"Glöckner H, Lucht LG. Weighted inversion of general Dirichlet series. <i>Transactions of the American Mathematical Society</i>. 2014;366(6):3275–3293. doi:<a href=\"https://doi.org/10.1090/S0002-9947-2013-06018-7\">10.1090/S0002-9947-2013-06018-7</a>"},"keyword":["11M41","30B50","30J99","46H99"],"language":[{"iso":"eng"}],"publication":"Transactions of the American Mathematical Society","date_created":"2026-02-26T10:56:00Z","title":"Weighted inversion of general Dirichlet series","quality_controlled":"1","issue":"6","year":"2014"},{"language":[{"iso":"eng"}],"_id":"51395","user_id":"49063","department":[{"_id":"91"}],"status":"public","type":"journal_article","publication":"J. London Math. 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Soc. 87 (2013) 561–585.","mla":"Hilgert, Joachim, et al. “Harmonic Analysis on Heisenberg-Clifford Lie Supergroups.” <i>J. London Math. Soc.</i>, vol. 87, 2013, pp. 561–85.","bibtex":"@article{Hilgert_Laubinger_Alldridge_2013, title={Harmonic analysis on Heisenberg-Clifford Lie supergroups}, volume={87}, journal={J. London Math. Soc.}, author={Hilgert, Joachim and Laubinger, M. and Alldridge, A.}, year={2013}, pages={561–585} }","apa":"Hilgert, J., Laubinger, M., &#38; Alldridge, A. (2013). Harmonic analysis on Heisenberg-Clifford Lie supergroups. <i>J. London Math. 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Hilgert, Lesebuch Mathematik für das erste Studienjahr, Springer Spektrum, 2013.","chicago":"Hilgert, Joachim. <i>Lesebuch Mathematik für das erste Studienjahr</i>. Springer Spektrum, 2013.","ieee":"J. Hilgert, <i>Lesebuch Mathematik für das erste Studienjahr</i>. Springer Spektrum, 2013.","ama":"Hilgert J. <i>Lesebuch Mathematik für das erste Studienjahr</i>. 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Experimental Observation of the Spectral Gap in Microwave n-Disk Systems. <i>Physical Review Letters</i>. 2013;110(16). doi:<a href=\"https://doi.org/10.1103/physrevlett.110.164102\">10.1103/physrevlett.110.164102</a>","ieee":"S. Barkhofen, T. Weich, A. Potzuweit, H.-J. Stöckmann, U. Kuhl, and M. Zworski, “Experimental Observation of the Spectral Gap in Microwave n-Disk Systems,” <i>Physical Review Letters</i>, vol. 110, no. 16, Art. no. 164102, 2013, doi: <a href=\"https://doi.org/10.1103/physrevlett.110.164102\">10.1103/physrevlett.110.164102</a>.","chicago":"Barkhofen, Sonja, Tobias Weich, A. Potzuweit, H.-J. Stöckmann, U. Kuhl, and M. Zworski. “Experimental Observation of the Spectral Gap in Microwave N-Disk Systems.” <i>Physical Review Letters</i> 110, no. 16 (2013). <a href=\"https://doi.org/10.1103/physrevlett.110.164102\">https://doi.org/10.1103/physrevlett.110.164102</a>.","bibtex":"@article{Barkhofen_Weich_Potzuweit_Stöckmann_Kuhl_Zworski_2013, title={Experimental Observation of the Spectral Gap in Microwave n-Disk Systems}, volume={110}, DOI={<a href=\"https://doi.org/10.1103/physrevlett.110.164102\">10.1103/physrevlett.110.164102</a>}, number={16164102}, journal={Physical Review Letters}, publisher={American Physical Society (APS)}, author={Barkhofen, Sonja and Weich, Tobias and Potzuweit, A. and Stöckmann, H.-J. and Kuhl, U. and Zworski, M.}, year={2013} }","short":"S. Barkhofen, T. Weich, A. Potzuweit, H.-J. Stöckmann, U. Kuhl, M. Zworski, Physical Review Letters 110 (2013).","mla":"Barkhofen, Sonja, et al. “Experimental Observation of the Spectral Gap in Microwave N-Disk Systems.” <i>Physical Review Letters</i>, vol. 110, no. 16, 164102, American Physical Society (APS), 2013, doi:<a href=\"https://doi.org/10.1103/physrevlett.110.164102\">10.1103/physrevlett.110.164102</a>.","apa":"Barkhofen, S., Weich, T., Potzuweit, A., Stöckmann, H.-J., Kuhl, U., &#38; Zworski, M. (2013). Experimental Observation of the Spectral Gap in Microwave n-Disk Systems. <i>Physical Review Letters</i>, <i>110</i>(16), Article 164102. <a href=\"https://doi.org/10.1103/physrevlett.110.164102\">https://doi.org/10.1103/physrevlett.110.164102</a>"},"intvolume":"       110","user_id":"48188","department":[{"_id":"10"},{"_id":"548"},{"_id":"288"}],"_id":"31298","article_number":"164102","type":"journal_article","status":"public","date_created":"2022-05-17T13:00:47Z","publisher":"American Physical Society (APS)","title":"Experimental Observation of the Spectral Gap in Microwave n-Disk Systems","issue":"16","year":"2013","external_id":{"arxiv":["1212.5897 "]},"language":[{"iso":"eng"}],"keyword":["General Physics and Astronomy"],"publication":"Physical Review Letters"},{"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>"}],"status":"public","publication":"Compositio Mathematica","type":"journal_article","keyword":["Algebra and Number Theory"],"language":[{"iso":"eng"}],"_id":"37672","department":[{"_id":"555"}],"user_id":"93826","year":"2013","page":"1381-1400","intvolume":"       149","citation":{"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.","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>","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>","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>.","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>."},"publication_identifier":{"issn":["0010-437X","1570-5846"]},"publication_status":"published","issue":"8","title":"Limit transition between hypergeometric functions of type BC and type A","doi":"10.1112/s0010437x13007045","publisher":"Wiley","date_updated":"2023-01-24T22:15:13Z","volume":149,"date_created":"2023-01-20T09:37:16Z","author":[{"last_name":"Rösler","id":"37390","full_name":"Rösler, Margit","first_name":"Margit"},{"first_name":"Tom","full_name":"Koornwinder, Tom","last_name":"Koornwinder"},{"full_name":"Voit, Michael","last_name":"Voit","first_name":"Michael"}]},{"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","last_name":"Rösler","full_name":"Rösler, Margit","id":"37390"},{"full_name":"Voit, Michael","last_name":"Voit","first_name":"Michael"}],"date_created":"2023-01-23T08:26:17Z","year":"2013","page":"899--920","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>","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>","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."},"publication_status":"published","issue":"4","language":[{"iso":"eng"}],"_id":"38038","department":[{"_id":"555"}],"user_id":"93826","status":"public","publication":"Journal of Lie Theory 23","type":"journal_article"},{"_id":"40072","user_id":"58312","department":[{"_id":"555"}],"extern":"1","type":"journal_article","status":"public","date_updated":"2023-01-26T17:29:16Z","author":[{"first_name":"Tomasz","last_name":"Luks","full_name":"Luks, Tomasz","id":"58312"}],"volume":39,"doi":"10.1007/s11118-012-9321-x","publication_status":"published","publication_identifier":{"issn":["0926-2601","1572-929X"]},"citation":{"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>","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>.","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>.","short":"T. Luks, Potential Analysis 39 (2013) 29–67.","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} }","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>"},"page":"29-67","intvolume":"        39","language":[{"iso":"eng"}],"publication":"Potential Analysis","publisher":"Springer Science and Business Media LLC","date_created":"2023-01-25T15:50:45Z","title":"Boundary Behavior of α-Harmonic Functions on the Complement of the Sphere and Hyperplane","issue":"1","year":"2013"}]