[{"title":"An uncertainty principle for the Dunkl transform","year":"1999","publication_identifier":{"issn":["0004-9727","1755-1633"]},"author":[{"last_name":"Rösler","first_name":"Margit","full_name":"Rösler, Margit","id":"37390"}],"publication_status":"published","date_updated":"2023-01-26T17:40:13Z","intvolume":"        59","language":[{"iso":"eng"}],"doi":"10.1017/s0004972700033025","issue":"3","publication":"Bulletin of the Australian Mathematical Society","extern":"1","abstract":[{"lang":"eng","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>"}],"date_created":"2023-01-26T08:19:30Z","type":"journal_article","keyword":["General Mathematics"],"department":[{"_id":"555"}],"status":"public","page":"353-360","publisher":"Cambridge University Press (CUP)","_id":"40184","user_id":"93826","volume":59,"citation":{"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>.","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>","short":"M. Rösler, Bulletin of the Australian Mathematical Society 59 (1999) 353–360.","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>.","mla":"Rösler, Margit. “An Uncertainty Principle for the Dunkl Transform.” <i>Bulletin of the Australian Mathematical Society</i>, vol. 59, no. 3, Cambridge University Press (CUP), 1999, pp. 353–60, doi:<a href=\"https://doi.org/10.1017/s0004972700033025\">10.1017/s0004972700033025</a>.","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} }","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>"}},{"status":"public","_id":"40189","publisher":"Duke University Press","page":"445-463","volume":98,"user_id":"93826","citation":{"short":"M. Rösler, Duke Mathematical Journal 98 (1999) 445–463.","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>.","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>","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>","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>."},"publication_identifier":{"issn":["0012-7094"]},"author":[{"last_name":"Rösler","first_name":"Margit","full_name":"Rösler, Margit","id":"37390"}],"title":"Positivity of Dunkl’s intertwining operator","year":"1999","intvolume":"        98","date_updated":"2023-01-26T17:40:05Z","publication_status":"published","language":[{"iso":"eng"}],"doi":"10.1215/s0012-7094-99-09813-7","issue":"3","publication":"Duke Mathematical Journal","extern":"1","date_created":"2023-01-26T08:25:43Z","department":[{"_id":"555"}],"type":"journal_article","keyword":["General Mathematics"]},{"date_created":"2023-01-26T08:27:14Z","department":[{"_id":"555"}],"keyword":["General Mathematics"],"type":"journal_article","publication":"Canadian Journal of Mathematics","issue":"1","extern":"1","abstract":[{"lang":"eng","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>"}],"language":[{"iso":"eng"}],"doi":"10.4153/cjm-1999-006-6","publication_identifier":{"issn":["0008-414X","1496-4279"]},"author":[{"last_name":"Rösler","first_name":"Margit","full_name":"Rösler, Margit","id":"37390"},{"full_name":"Voit, Michael","first_name":"Michael","last_name":"Voit"}],"title":"Partial Characters and Signed Quotient Hypergroups","year":"1999","intvolume":"        51","publication_status":"published","date_updated":"2023-01-26T17:51:42Z","citation":{"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} }","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>","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>.","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>.","short":"M. Rösler, M. Voit, Canadian Journal of Mathematics 51 (1999) 96–116.","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>.","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>"},"_id":"40192","publisher":"Canadian Mathematical Society","page":"96-116","volume":51,"user_id":"37390","status":"public"},{"citation":{"apa":"Rösler, M., &#38; Voit, M. (1999). An uncertainty principle for Hankel transforms. <i>Proceedings of the American Mathematical Society</i>, <i>127</i>(1), 183–194.","ieee":"M. Rösler and M. 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An uncertainty principle for Hankel transforms. <i>Proceedings of the American Mathematical Society</i>. 1999;127(1):183–194.","bibtex":"@article{Rösler_Voit_1999, title={An uncertainty principle for Hankel transforms}, volume={127}, number={1}, journal={Proceedings of the American Mathematical Society}, publisher={American Mathematical Society (AMS)}, author={Rösler, Margit and Voit, Michael}, year={1999}, pages={183–194} }"},"page":"183–194","publisher":"American Mathematical Society (AMS)","_id":"40666","user_id":"37390","volume":127,"status":"public","date_created":"2023-01-30T11:20:49Z","type":"journal_article","department":[{"_id":"555"}],"issue":"1","publication":"Proceedings of the American Mathematical Society","extern":"1","language":[{"iso":"eng"}],"title":"An uncertainty principle for Hankel transforms","year":"1999","publication_identifier":{"issn":["0002-9939","1088-6826"]},"author":[{"full_name":"Rösler, Margit","last_name":"Rösler","first_name":"Margit","id":"37390"},{"full_name":"Voit, Michael","last_name":"Voit","first_name":"Michael"}],"publication_status":"published","date_updated":"2025-08-09T09:24:57Z","intvolume":"       127"},{"type":"book_chapter","department":[{"_id":"91"}],"date_created":"2024-02-19T10:00:45Z","place":"Berlin","extern":"1","publication":"Positivity in Lie Theory: Open Problems","citation":{"mla":"Hilgert, Joachim, and K. 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Bertram. “Hardy Spaces and Analytic Continuation of Bergman Spaces.” <i>Bull. Math. Soc. Francaise</i> 126 (1998): 435–82.","short":"J. Hilgert, W. Bertram, Bull. Math. Soc. Francaise 126 (1998) 435–482."},"extern":"1"},{"type":"journal_article","department":[{"_id":"91"}],"date_created":"2024-02-19T07:19:27Z","extern":"1","publication":"Math. Nachr.","citation":{"chicago":"Hilgert, Joachim, and K.-H. Neeb. “Poisson Lie Groups and Non-Linear Convexity Theorems.” <i>Math. Nachr.</i> 191 (1998): 153–87.","short":"J. Hilgert, K.-H. Neeb, Math. Nachr. 191 (1998) 153–187.","apa":"Hilgert, J., &#38; Neeb, K.-H. (1998). Poisson Lie Groups and Non-Linear Convexity Theorems. <i>Math. Nachr.</i>, <i>191</i>, 153–187.","ieee":"J. Hilgert and K.-H. Neeb, “Poisson Lie Groups and Non-Linear Convexity Theorems,” <i>Math. Nachr.</i>, vol. 191, pp. 153–187, 1998.","ama":"Hilgert J, Neeb K-H. 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