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Deitmar, (2004).","mla":"Hilgert, Joachim, and A. Deitmar. <i>The Lewis Correspondence for Submodular Groups</i>. 2004.","bibtex":"@article{Hilgert_Deitmar_2004, title={The Lewis Correspondence for submodular groups}, author={Hilgert, Joachim and Deitmar, A.}, year={2004} }","ama":"Hilgert J, Deitmar A. The Lewis Correspondence for submodular groups. Published online 2004.","ieee":"J. Hilgert and A. Deitmar, “The Lewis Correspondence for submodular groups.” 2004.","chicago":"Hilgert, Joachim, and A. Deitmar. “The Lewis Correspondence for Submodular Groups,” 2004."},"_id":"51548","user_id":"49063","department":[{"_id":"91"}],"extern":"1","language":[{"iso":"eng"}],"type":"preprint","status":"public"},{"publication":"International Mathematics Research Notices","type":"journal_article","status":"public","abstract":[{"lang":"eng","text":"In this note, a new proof for the positivity of Dunkl's intertwining operator in the crystallographic case is given. It is based on an asymptotic relationship between the Opdam-Cherednik kernel and the Dunkl kernel as recently observed by M. de Jeu, and on positivity results of S. Sahi for the Heckman-Opdam polynomials and their non-symmetric counterparts."}],"department":[{"_id":"555"}],"user_id":"93826","_id":"40320","extern":"1","language":[{"iso":"eng"}],"issue":"63","publication_identifier":{"issn":["1073-7928","1687-0247"]},"publication_status":"published","page":"3379–3389","citation":{"ama":"Rösler M, Voit M. Positivity of Dunkl’s intertwining operator via the trigonometric setting. <i>International Mathematics Research Notices</i>. 2004;(63):3379–3389. doi:<a href=\"https://doi.org/10.48550/ARXIV.MATH/0405368\">10.48550/ARXIV.MATH/0405368</a>","chicago":"Rösler, Margit, and Michael Voit. “Positivity of Dunkl’s Intertwining Operator via the Trigonometric Setting.” <i>International Mathematics Research Notices</i>, no. 63 (2004): 3379–3389. <a href=\"https://doi.org/10.48550/ARXIV.MATH/0405368\">https://doi.org/10.48550/ARXIV.MATH/0405368</a>.","ieee":"M. Rösler and M. Voit, “Positivity of Dunkl’s intertwining operator via the trigonometric setting,” <i>International Mathematics Research Notices</i>, no. 63, pp. 3379–3389, 2004, doi: <a href=\"https://doi.org/10.48550/ARXIV.MATH/0405368\">10.48550/ARXIV.MATH/0405368</a>.","apa":"Rösler, M., &#38; Voit, M. (2004). 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Voit, International Mathematics Research Notices (2004) 3379–3389.","mla":"Rösler, Margit, and Michael Voit. “Positivity of Dunkl’s Intertwining Operator via the Trigonometric Setting.” <i>International Mathematics Research Notices</i>, no. 63, Oxford University Press, 2004, pp. 3379–3389, doi:<a href=\"https://doi.org/10.48550/ARXIV.MATH/0405368\">10.48550/ARXIV.MATH/0405368</a>.","bibtex":"@article{Rösler_Voit_2004, title={Positivity of Dunkl’s intertwining operator via the trigonometric setting}, DOI={<a href=\"https://doi.org/10.48550/ARXIV.MATH/0405368\">10.48550/ARXIV.MATH/0405368</a>}, number={63}, journal={International Mathematics Research Notices}, publisher={Oxford University Press}, author={Rösler, Margit and Voit, Michael}, year={2004}, pages={3379–3389} }"},"year":"2004","date_created":"2023-01-26T11:05:33Z","author":[{"first_name":"Margit","last_name":"Rösler","full_name":"Rösler, Margit","id":"37390"},{"first_name":"Michael","last_name":"Voit","full_name":"Voit, Michael"}],"publisher":"Oxford University Press","date_updated":"2023-01-26T17:28:09Z","doi":"10.48550/ARXIV.MATH/0405368","title":"Positivity of Dunkl's intertwining operator via the trigonometric setting"},{"year":"2004","page":"1–16","citation":{"ama":"Glöckner H. 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Tensor products in the category of topological vector spaces are not associative. <i>Commentationes Mathematicae Universitatis Carolinae</i>, <i>45</i>(4), 607–614.","bibtex":"@article{Glöckner_2004, title={Tensor products in the category of topological vector spaces are not associative.}, volume={45}, number={4}, journal={Commentationes Mathematicae Universitatis Carolinae}, author={Glöckner, Helge}, year={2004}, pages={607–614} }","mla":"Glöckner, Helge. “Tensor Products in the Category of Topological Vector Spaces Are Not Associative.” <i>Commentationes Mathematicae Universitatis Carolinae</i>, vol. 45, no. 4, 2004, pp. 607–614.","short":"H. Glöckner, Commentationes Mathematicae Universitatis Carolinae 45 (2004) 607–614.","ama":"Glöckner H. Tensor products in the category of topological vector spaces are not associative. <i>Commentationes Mathematicae Universitatis Carolinae</i>. 2004;45(4):607–614.","ieee":"H. 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Hilgert, E.B. Vinberg, A. Pasquale, AMS Translations 210 (2003) 135–143.","apa":"Hilgert, J., Vinberg, E. B., &#38; Pasquale, A. (2003). The Dual Horospherical Radon Transform as a Limit of Spherical Radon Transforms. <i>AMS Translations</i>, <i>210</i>, 135–143.","ama":"Hilgert J, Vinberg EB, Pasquale A. The Dual Horospherical Radon Transform as a Limit of Spherical Radon Transforms. <i>AMS Translations</i>. 2003;210:135-143.","ieee":"J. Hilgert, E. B. Vinberg, and A. Pasquale, “The Dual Horospherical Radon Transform as a Limit of Spherical Radon Transforms,” <i>AMS Translations</i>, vol. 210, pp. 135–143, 2003.","chicago":"Hilgert, Joachim, E.B. Vinberg, and A. 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In: <i>Lecture Notes in Mathematics</i>. Springer Berlin Heidelberg; 2003:93–135. doi:<a href=\"https://doi.org/10.1007/3-540-44945-0_3\">10.1007/3-540-44945-0_3</a>","chicago":"Rösler, Margit. “Dunkl Operators: Theory and Applications.” In <i>Lecture Notes in Mathematics</i>, 93–135. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. <a href=\"https://doi.org/10.1007/3-540-44945-0_3\">https://doi.org/10.1007/3-540-44945-0_3</a>.","ieee":"M. Rösler, “Dunkl Operators: Theory and Applications,” in <i>Lecture Notes in Mathematics</i>, Berlin, Heidelberg: Springer Berlin Heidelberg, 2003, pp. 93–135.","mla":"Rösler, Margit. “Dunkl Operators: Theory and Applications.” <i>Lecture Notes in Mathematics</i>, Springer Berlin Heidelberg, 2003, pp. 93–135, doi:<a href=\"https://doi.org/10.1007/3-540-44945-0_3\">10.1007/3-540-44945-0_3</a>.","bibtex":"@inbook{Rösler_2003, place={Berlin, Heidelberg}, title={Dunkl Operators: Theory and Applications}, DOI={<a href=\"https://doi.org/10.1007/3-540-44945-0_3\">10.1007/3-540-44945-0_3</a>}, booktitle={Lecture Notes in Mathematics}, publisher={Springer Berlin Heidelberg}, author={Rösler, Margit}, year={2003}, pages={93–135} }","short":"M. Rösler, in: Lecture Notes in Mathematics, Springer Berlin Heidelberg, Berlin, Heidelberg, 2003, pp. 93–135.","apa":"Rösler, M. (2003). Dunkl Operators: Theory and Applications. In <i>Lecture Notes in Mathematics</i> (pp. 93–135). Springer Berlin Heidelberg. <a href=\"https://doi.org/10.1007/3-540-44945-0_3\">https://doi.org/10.1007/3-540-44945-0_3</a>"},"page":"93–135","year":"2003","place":"Berlin, Heidelberg","date_created":"2023-01-25T10:09:14Z","author":[{"first_name":"Margit","last_name":"Rösler","full_name":"Rösler, Margit","id":"37390"}],"date_updated":"2023-01-26T17:44:19Z","publisher":"Springer Berlin Heidelberg","doi":"10.1007/3-540-44945-0_3","title":"Dunkl Operators: Theory and Applications"},{"issue":"6","year":"2003","publisher":"American Mathematical Society (AMS)","date_created":"2023-01-25T10:17:51Z","title":"A positive radial product formula for the Dunkl kernel","publication":"Transactions of the American Mathematical Society","abstract":[{"lang":"eng","text":"It is an open conjecture that generalized Bessel functions associated with root systems have a positive product formula for non-negative multiplicity parameters of the associated Dunkl operators. In this paper, a partial result towards this conjecture is proven, namely a positive radial product formula for the non-symmetric counterpart of the generalized Bessel function, the Dunkl kernel. Radial hereby means that one of the factors in the product formula is replaced by its mean over a sphere. The key to this product formula is a positivity result for the Dunkl-type spherical mean operator. It can also be interpreted in the sense that the Dunkl-type generalized translation of radial functions is positivity-preserving. As an application, we construct Dunkl-type homogeneous Markov processes associated with radial probability distributions."}],"language":[{"iso":"eng"}],"publication_status":"published","citation":{"short":"M. Rösler, Transactions of the American Mathematical Society 355 (2003) 2413–2438.","bibtex":"@article{Rösler_2003, title={A positive radial product formula for the Dunkl kernel}, volume={355}, DOI={<a href=\"https://doi.org/10.48550/ARXIV.MATH/0210137\">10.48550/ARXIV.MATH/0210137</a>}, number={6}, journal={Transactions of the American Mathematical Society}, publisher={American Mathematical Society (AMS)}, author={Rösler, Margit}, year={2003}, pages={2413–2438} }","mla":"Rösler, Margit. “A Positive Radial Product Formula for the Dunkl Kernel.” <i>Transactions of the American Mathematical Society</i>, vol. 355, no. 6, American Mathematical Society (AMS), 2003, pp. 2413–2438, doi:<a href=\"https://doi.org/10.48550/ARXIV.MATH/0210137\">10.48550/ARXIV.MATH/0210137</a>.","apa":"Rösler, M. (2003). A positive radial product formula for the Dunkl kernel. <i>Transactions of the American Mathematical Society</i>, <i>355</i>(6), 2413–2438. <a href=\"https://doi.org/10.48550/ARXIV.MATH/0210137\">https://doi.org/10.48550/ARXIV.MATH/0210137</a>","ama":"Rösler M. A positive radial product formula for the Dunkl kernel. <i>Transactions of the American Mathematical Society</i>. 2003;355(6):2413–2438. doi:<a href=\"https://doi.org/10.48550/ARXIV.MATH/0210137\">10.48550/ARXIV.MATH/0210137</a>","ieee":"M. Rösler, “A positive radial product formula for the Dunkl kernel,” <i>Transactions of the American Mathematical Society</i>, vol. 355, no. 6, pp. 2413–2438, 2003, doi: <a href=\"https://doi.org/10.48550/ARXIV.MATH/0210137\">10.48550/ARXIV.MATH/0210137</a>.","chicago":"Rösler, Margit. “A Positive Radial Product Formula for the Dunkl Kernel.” <i>Transactions of the American Mathematical Society</i> 355, no. 6 (2003): 2413–2438. <a href=\"https://doi.org/10.48550/ARXIV.MATH/0210137\">https://doi.org/10.48550/ARXIV.MATH/0210137</a>."},"page":"2413–2438","intvolume":"       355","date_updated":"2023-01-26T17:44:10Z","author":[{"first_name":"Margit","last_name":"Rösler","id":"37390","full_name":"Rösler, Margit"}],"volume":355,"doi":"10.48550/ARXIV.MATH/0210137","type":"journal_article","status":"public","_id":"39957","user_id":"93826","department":[{"_id":"555"}],"extern":"1"}]