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Representations, Characters, and Spherical Functions Associated to Causal Symmetric Spaces. <i>J Funct Anal</i>. 1999;169:357-390.","ieee":"J. Hilgert and B. Krötz, “Representations, Characters, and Spherical Functions Associated to Causal Symmetric Spaces,” <i>J. Funct. Anal.</i>, vol. 169, pp. 357–390, 1999.","chicago":"Hilgert, Joachim, and B. Krötz. “Representations, Characters, and Spherical Functions Associated to Causal Symmetric Spaces.” <i>J. Funct. Anal.</i> 169 (1999): 357–90.","apa":"Hilgert, J., &#38; Krötz, B. (1999). Representations, Characters, and Spherical Functions Associated to Causal Symmetric Spaces. <i>J. Funct. Anal.</i>, <i>169</i>, 357–390.","mla":"Hilgert, Joachim, and B. Krötz. “Representations, Characters, and Spherical Functions Associated to Causal Symmetric Spaces.” <i>J. Funct. 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Neumann , G. Ólafsson, Math. Annalen 313 (1999) 785–791.","bibtex":"@article{Hilgert_Neumann _Ólafsson_1999, title={A Conjugacy Theorem for Symmetric Spaces}, volume={313}, journal={Math. Annalen}, author={Hilgert, Joachim and Neumann , A. and Ólafsson, G.}, year={1999}, pages={785–791} }","apa":"Hilgert, J., Neumann , A., &#38; Ólafsson, G. (1999). A Conjugacy Theorem for Symmetric Spaces. <i>Math. Annalen</i>, <i>313</i>, 785–791."},"year":"1999","publication_status":"published","title":"A Conjugacy Theorem for Symmetric Spaces","volume":313,"date_created":"2024-02-19T07:17:56Z","author":[{"first_name":"Joachim","id":"220","full_name":"Hilgert, Joachim","last_name":"Hilgert"},{"first_name":"A.","full_name":"Neumann , A.","last_name":"Neumann "},{"first_name":"G.","full_name":"Ólafsson, G.","last_name":"Ólafsson"}],"date_updated":"2024-02-20T13:30:50Z","status":"public","publication":"Math. Annalen","type":"journal_article","language":[{"iso":"eng"}],"extern":"1","department":[{"_id":"91"}],"user_id":"49063","_id":"51424"},{"title":"Weighted Bergman Spaces Associated to Causal Symmetric Spaces","date_updated":"2024-02-20T13:31:09Z","volume":99,"author":[{"id":"220","full_name":"Hilgert, Joachim","last_name":"Hilgert","first_name":"Joachim"},{"first_name":"B.","last_name":"Krötz","full_name":"Krötz, B."}],"date_created":"2024-02-19T07:16:14Z","year":"1999","page":"151-180","intvolume":"        99","citation":{"bibtex":"@article{Hilgert_Krötz_1999, title={Weighted Bergman Spaces Associated to Causal Symmetric Spaces}, volume={99}, journal={Manus. Math.}, author={Hilgert, Joachim and Krötz, B.}, year={1999}, pages={151–180} }","mla":"Hilgert, Joachim, and B. Krötz. “Weighted Bergman Spaces Associated to Causal Symmetric Spaces.” <i>Manus. Math.</i>, vol. 99, 1999, pp. 151–80.","short":"J. Hilgert, B. Krötz, Manus. Math. 99 (1999) 151–180.","apa":"Hilgert, J., &#38; Krötz, B. (1999). Weighted Bergman Spaces Associated to Causal Symmetric Spaces. <i>Manus. Math.</i>, <i>99</i>, 151–180.","chicago":"Hilgert, Joachim, and B. Krötz. “Weighted Bergman Spaces Associated to Causal Symmetric Spaces.” <i>Manus. Math.</i> 99 (1999): 151–80.","ieee":"J. Hilgert and B. Krötz, “Weighted Bergman Spaces Associated to Causal Symmetric Spaces,” <i>Manus. Math.</i>, vol. 99, pp. 151–180, 1999.","ama":"Hilgert J, Krötz B. Weighted Bergman Spaces Associated to Causal Symmetric Spaces. <i>Manus Math</i>. 1999;99:151-180."},"publication_status":"published","language":[{"iso":"eng"}],"extern":"1","_id":"51423","department":[{"_id":"91"}],"user_id":"49063","status":"public","publication":"Manus. Math.","type":"journal_article"},{"page":"1345-1380","intvolume":"       352","citation":{"ama":"Hilgert J, Neeb K-H. Positive Definite Spherical Functions on Olshanskii Domains. <i>Trans AMS</i>. 1999;352:1345-1380.","ieee":"J. Hilgert and K.-H. Neeb, “Positive Definite Spherical Functions on Olshanskii Domains,” <i>Trans. AMS.</i>, vol. 352, pp. 1345–1380, 1999.","chicago":"Hilgert, Joachim, and K.-H. Neeb. “Positive Definite Spherical Functions on Olshanskii Domains.” <i>Trans. AMS.</i> 352 (1999): 1345–80.","short":"J. Hilgert, K.-H. Neeb, Trans. AMS. 352 (1999) 1345–1380.","bibtex":"@article{Hilgert_Neeb_1999, title={Positive Definite Spherical Functions on Olshanskii Domains}, volume={352}, journal={Trans. AMS.}, author={Hilgert, Joachim and Neeb, K.-H.}, year={1999}, pages={1345–1380} }","mla":"Hilgert, Joachim, and K. H. Neeb. “Positive Definite Spherical Functions on Olshanskii Domains.” <i>Trans. AMS.</i>, vol. 352, 1999, pp. 1345–80.","apa":"Hilgert, J., &#38; Neeb, K.-H. (1999). Positive Definite Spherical Functions on Olshanskii Domains. <i>Trans. 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Rösler, Bulletin of the Australian Mathematical Society 59 (1999) 353–360.","bibtex":"@article{Rösler_1999, title={An uncertainty principle for the Dunkl transform}, volume={59}, DOI={<a href=\"https://doi.org/10.1017/s0004972700033025\">10.1017/s0004972700033025</a>}, number={3}, journal={Bulletin of the Australian Mathematical Society}, publisher={Cambridge University Press (CUP)}, author={Rösler, Margit}, year={1999}, pages={353–360} }","apa":"Rösler, M. (1999). An uncertainty principle for the Dunkl transform. <i>Bulletin of the Australian Mathematical Society</i>, <i>59</i>(3), 353–360. <a href=\"https://doi.org/10.1017/s0004972700033025\">https://doi.org/10.1017/s0004972700033025</a>","ama":"Rösler M. An uncertainty principle for the Dunkl transform. <i>Bulletin of the Australian Mathematical Society</i>. 1999;59(3):353-360. doi:<a href=\"https://doi.org/10.1017/s0004972700033025\">10.1017/s0004972700033025</a>","chicago":"Rösler, Margit. “An Uncertainty Principle for the Dunkl Transform.” <i>Bulletin of the Australian Mathematical Society</i> 59, no. 3 (1999): 353–60. <a href=\"https://doi.org/10.1017/s0004972700033025\">https://doi.org/10.1017/s0004972700033025</a>.","ieee":"M. Rösler, “An uncertainty principle for the Dunkl transform,” <i>Bulletin of the Australian Mathematical Society</i>, vol. 59, no. 3, pp. 353–360, 1999, doi: <a href=\"https://doi.org/10.1017/s0004972700033025\">10.1017/s0004972700033025</a>."},"page":"353-360","intvolume":"        59","author":[{"full_name":"Rösler, Margit","id":"37390","last_name":"Rösler","first_name":"Margit"}],"volume":59,"date_updated":"2023-01-26T17:40:13Z","doi":"10.1017/s0004972700033025","type":"journal_article","status":"public","user_id":"93826","department":[{"_id":"555"}],"_id":"40184","extern":"1","issue":"3","year":"1999","date_created":"2023-01-26T08:19:30Z","publisher":"Cambridge University Press (CUP)","title":"An uncertainty principle for the Dunkl transform","publication":"Bulletin of the Australian Mathematical Society","abstract":[{"text":"<jats:p>This note presents an analogue of the classical Heisenberg-Weyl uncertainty principle for the Dunkl transform on ℝ<jats:sup><jats:italic>N</jats:italic></jats:sup>. Its proof is based on expansions with respect to generalised Hermite functions.</jats:p>","lang":"eng"}],"language":[{"iso":"eng"}],"keyword":["General Mathematics"]},{"volume":98,"author":[{"last_name":"Rösler","full_name":"Rösler, Margit","id":"37390","first_name":"Margit"}],"date_updated":"2023-01-26T17:40:05Z","doi":"10.1215/s0012-7094-99-09813-7","publication_identifier":{"issn":["0012-7094"]},"publication_status":"published","intvolume":"        98","page":"445-463","citation":{"chicago":"Rösler, Margit. “Positivity of Dunkl’s Intertwining Operator.” <i>Duke Mathematical Journal</i> 98, no. 3 (1999): 445–63. <a href=\"https://doi.org/10.1215/s0012-7094-99-09813-7\">https://doi.org/10.1215/s0012-7094-99-09813-7</a>.","ieee":"M. Rösler, “Positivity of Dunkl’s intertwining operator,” <i>Duke Mathematical Journal</i>, vol. 98, no. 3, pp. 445–463, 1999, doi: <a href=\"https://doi.org/10.1215/s0012-7094-99-09813-7\">10.1215/s0012-7094-99-09813-7</a>.","ama":"Rösler M. Positivity of Dunkl’s intertwining operator. <i>Duke Mathematical Journal</i>. 1999;98(3):445-463. doi:<a href=\"https://doi.org/10.1215/s0012-7094-99-09813-7\">10.1215/s0012-7094-99-09813-7</a>","apa":"Rösler, M. (1999). Positivity of Dunkl’s intertwining operator. <i>Duke Mathematical Journal</i>, <i>98</i>(3), 445–463. <a href=\"https://doi.org/10.1215/s0012-7094-99-09813-7\">https://doi.org/10.1215/s0012-7094-99-09813-7</a>","short":"M. Rösler, Duke Mathematical Journal 98 (1999) 445–463.","bibtex":"@article{Rösler_1999, title={Positivity of Dunkl’s intertwining operator}, volume={98}, DOI={<a href=\"https://doi.org/10.1215/s0012-7094-99-09813-7\">10.1215/s0012-7094-99-09813-7</a>}, number={3}, journal={Duke Mathematical Journal}, publisher={Duke University Press}, author={Rösler, Margit}, year={1999}, pages={445–463} }","mla":"Rösler, Margit. “Positivity of Dunkl’s Intertwining Operator.” <i>Duke Mathematical Journal</i>, vol. 98, no. 3, Duke University Press, 1999, pp. 445–63, doi:<a href=\"https://doi.org/10.1215/s0012-7094-99-09813-7\">10.1215/s0012-7094-99-09813-7</a>."},"department":[{"_id":"555"}],"user_id":"93826","_id":"40189","extern":"1","type":"journal_article","status":"public","date_created":"2023-01-26T08:25:43Z","publisher":"Duke University Press","title":"Positivity of Dunkl’s intertwining operator","issue":"3","year":"1999","language":[{"iso":"eng"}],"keyword":["General Mathematics"],"publication":"Duke Mathematical Journal"},{"volume":51,"author":[{"id":"37390","full_name":"Rösler, Margit","last_name":"Rösler","first_name":"Margit"},{"full_name":"Voit, Michael","last_name":"Voit","first_name":"Michael"}],"date_created":"2023-01-26T08:27:14Z","publisher":"Canadian Mathematical Society","date_updated":"2023-01-26T17:51:42Z","doi":"10.4153/cjm-1999-006-6","title":"Partial Characters and Signed Quotient Hypergroups","issue":"1","publication_identifier":{"issn":["0008-414X","1496-4279"]},"publication_status":"published","intvolume":"        51","page":"96-116","citation":{"chicago":"Rösler, Margit, and Michael Voit. “Partial Characters and Signed Quotient Hypergroups.” <i>Canadian Journal of Mathematics</i> 51, no. 1 (1999): 96–116. <a href=\"https://doi.org/10.4153/cjm-1999-006-6\">https://doi.org/10.4153/cjm-1999-006-6</a>.","ieee":"M. Rösler and M. Voit, “Partial Characters and Signed Quotient Hypergroups,” <i>Canadian Journal of Mathematics</i>, vol. 51, no. 1, pp. 96–116, 1999, doi: <a href=\"https://doi.org/10.4153/cjm-1999-006-6\">10.4153/cjm-1999-006-6</a>.","ama":"Rösler M, Voit M. Partial Characters and Signed Quotient Hypergroups. <i>Canadian Journal of Mathematics</i>. 1999;51(1):96-116. doi:<a href=\"https://doi.org/10.4153/cjm-1999-006-6\">10.4153/cjm-1999-006-6</a>","apa":"Rösler, M., &#38; Voit, M. (1999). Partial Characters and Signed Quotient Hypergroups. <i>Canadian Journal of Mathematics</i>, <i>51</i>(1), 96–116. <a href=\"https://doi.org/10.4153/cjm-1999-006-6\">https://doi.org/10.4153/cjm-1999-006-6</a>","bibtex":"@article{Rösler_Voit_1999, title={Partial Characters and Signed Quotient Hypergroups}, volume={51}, DOI={<a href=\"https://doi.org/10.4153/cjm-1999-006-6\">10.4153/cjm-1999-006-6</a>}, number={1}, journal={Canadian Journal of Mathematics}, publisher={Canadian Mathematical Society}, author={Rösler, Margit and Voit, Michael}, year={1999}, pages={96–116} }","short":"M. Rösler, M. Voit, Canadian Journal of Mathematics 51 (1999) 96–116.","mla":"Rösler, Margit, and Michael Voit. “Partial Characters and Signed Quotient Hypergroups.” <i>Canadian Journal of Mathematics</i>, vol. 51, no. 1, Canadian Mathematical Society, 1999, pp. 96–116, doi:<a href=\"https://doi.org/10.4153/cjm-1999-006-6\">10.4153/cjm-1999-006-6</a>."},"year":"1999","department":[{"_id":"555"}],"user_id":"37390","_id":"40192","extern":"1","language":[{"iso":"eng"}],"keyword":["General Mathematics"],"publication":"Canadian Journal of Mathematics","type":"journal_article","status":"public","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>If<jats:italic>G</jats:italic>is a closed subgroup of a commutative hypergroup<jats:italic>K</jats:italic>, then the coset space<jats:italic>K</jats:italic>/<jats:italic>G</jats:italic>carries a quotient hypergroup structure. In this paper, we study related convolution structures on<jats:italic>K</jats:italic>/<jats:italic>G</jats:italic>coming fromdeformations of the quotient hypergroup structure by certain functions on<jats:italic>K</jats:italic>which we call partial characters with respect to<jats:italic>G</jats:italic>. They are usually not probability-preserving, but lead to so-called signed hypergroups on<jats:italic>K</jats:italic>/<jats:italic>G</jats:italic>. A first example is provided by the Laguerre convolution on [0, ∞[, which is interpreted as a signed quotient hypergroup convolution derived from the Heisenberg group. Moreover, signed hypergroups associated with the Gelfand pair (<jats:italic>U</jats:italic>(<jats:italic>n</jats:italic>, 1),<jats:italic>U</jats:italic>(<jats:italic>n</jats:italic>)) are discussed.</jats:p>","lang":"eng"}]}]