{"year":"2003","title":"A positive radial product formula for the Dunkl kernel","publication_status":"published","user_id":"93826","language":[{"iso":"eng"}],"type":"journal_article","intvolume":"       355","abstract":[{"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.","lang":"eng"}],"page":"2413–2438","_id":"39957","status":"public","date_updated":"2023-01-26T17:44:10Z","date_created":"2023-01-25T10:17:51Z","volume":355,"issue":"6","author":[{"first_name":"Margit","id":"37390","last_name":"Rösler","full_name":"Rösler, Margit"}],"publisher":"American Mathematical Society (AMS)","department":[{"_id":"555"}],"publication":"Transactions of the American Mathematical Society","citation":{"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>.","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} }","short":"M. Rösler, Transactions of the American Mathematical Society 355 (2003) 2413–2438.","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>","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>","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>."},"doi":"10.48550/ARXIV.MATH/0210137","extern":"1"}