{"publication_status":"published","abstract":[{"text":"<jats:title>Abstract</jats:title>\r\n               <jats:p>Let $V_k$ denote Dunkl’s intertwining operator associated with some root system $R$ and multiplicity $k$. For two multiplicities $k, k^{\\prime }$ on $R$, we study the intertwiner $V_{k^{\\prime },k} = V_{k^{\\prime }}\\circ V_k^{-1}$ between Dunkl operators with multiplicities $k$ and $k^{\\prime }.$ It has been a long-standing conjecture that $V_{k^{\\prime },k}$ is positive if $k^{\\prime } \\geq k \\geq 0.$ We disprove this conjecture by constructing counterexamples for root system $B_n$. This matter is closely related to the existence of Sonine-type integral representations between Dunkl kernels and Bessel functions with different multiplicities. In our examples, such Sonine formulas do not exist. As a consequence, we obtain necessary conditions on Sonine formulas for Heckman–Opdam hypergeometric functions of type $BC_n$ and conditions for positive branching coefficients between multivariable Jacobi polynomials.</jats:p>","lang":"eng"}],"title":"Sonine Formulas and Intertwining Operators in Dunkl Theory","publication":"International Mathematics Research Notices","date_updated":"2023-01-24T22:16:12Z","author":[{"last_name":"Rösler","full_name":"Rösler, Margit","first_name":"Margit","id":"37390"},{"first_name":"Michael","full_name":"Voit, Michael","last_name":"Voit"}],"volume":2021,"year":"2021","_id":"37649","intvolume":"      2021","language":[{"iso":"eng"}],"keyword":["General Mathematics"],"publication_identifier":{"issn":["1073-7928","1687-0247"]},"page":"13202-13230","status":"public","type":"journal_article","issue":"17","doi":"10.1093/imrn/rnz313","citation":{"short":"M. Rösler, M. Voit, International Mathematics Research Notices 2021 (2021) 13202–13230.","chicago":"Rösler, Margit, and Michael Voit. “Sonine Formulas and Intertwining Operators in Dunkl Theory.” <i>International Mathematics Research Notices</i> 2021, no. 17 (2021): 13202–30. <a href=\"https://doi.org/10.1093/imrn/rnz313\">https://doi.org/10.1093/imrn/rnz313</a>.","apa":"Rösler, M., &#38; Voit, M. (2021). Sonine Formulas and Intertwining Operators in Dunkl Theory. <i>International Mathematics Research Notices</i>, <i>2021</i>(17), 13202–13230. <a href=\"https://doi.org/10.1093/imrn/rnz313\">https://doi.org/10.1093/imrn/rnz313</a>","mla":"Rösler, Margit, and Michael Voit. “Sonine Formulas and Intertwining Operators in Dunkl Theory.” <i>International Mathematics Research Notices</i>, vol. 2021, no. 17, Oxford University Press (OUP), 2021, pp. 13202–30, doi:<a href=\"https://doi.org/10.1093/imrn/rnz313\">10.1093/imrn/rnz313</a>.","ieee":"M. Rösler and M. Voit, “Sonine Formulas and Intertwining Operators in Dunkl Theory,” <i>International Mathematics Research Notices</i>, vol. 2021, no. 17, pp. 13202–13230, 2021, doi: <a href=\"https://doi.org/10.1093/imrn/rnz313\">10.1093/imrn/rnz313</a>.","ama":"Rösler M, Voit M. Sonine Formulas and Intertwining Operators in Dunkl Theory. <i>International Mathematics Research Notices</i>. 2021;2021(17):13202-13230. doi:<a href=\"https://doi.org/10.1093/imrn/rnz313\">10.1093/imrn/rnz313</a>","bibtex":"@article{Rösler_Voit_2021, title={Sonine Formulas and Intertwining Operators in Dunkl Theory}, volume={2021}, DOI={<a href=\"https://doi.org/10.1093/imrn/rnz313\">10.1093/imrn/rnz313</a>}, number={17}, journal={International Mathematics Research Notices}, publisher={Oxford University Press (OUP)}, author={Rösler, Margit and Voit, Michael}, year={2021}, pages={13202–13230} }"},"publisher":"Oxford University Press (OUP)","user_id":"37390","date_created":"2023-01-20T08:50:07Z"}