[{"user_id":"55911","department":[{"_id":"555"}],"_id":"56366","language":[{"iso":"eng"}],"type":"journal_article","publication":"Mathematische Nachrichten","status":"public","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>We discuss in which cases the Dunkl convolution  of distributions , possibly both with non‐compact support, can be defined and study its analytic properties. We prove results on the (singular‐)support of Dunkl convolutions. Based on this, we are able to prove a theorem on elliptic regularity for a certain class of Dunkl operators, called elliptic Dunkl operators. Finally, for the root system  we consider the Riesz distributions  and prove that their Dunkl convolution exists and that  holds.</jats:p>","lang":"eng"}],"date_created":"2024-10-07T11:44:00Z","author":[{"last_name":"Brennecken","full_name":"Brennecken, Dominik","id":"55911","first_name":"Dominik"}],"date_updated":"2024-10-07T11:46:15Z","publisher":"Wiley","doi":"10.1002/mana.202300370","title":"Dunkl convolution and elliptic regularity for Dunkl operators","publication_status":"published","publication_identifier":{"issn":["0025-584X","1522-2616"]},"citation":{"chicago":"Brennecken, Dominik. “Dunkl Convolution and Elliptic Regularity for Dunkl Operators.” <i>Mathematische Nachrichten</i>, 2024. <a href=\"https://doi.org/10.1002/mana.202300370\">https://doi.org/10.1002/mana.202300370</a>.","ieee":"D. Brennecken, “Dunkl convolution and elliptic regularity for Dunkl operators,” <i>Mathematische Nachrichten</i>, 2024, doi: <a href=\"https://doi.org/10.1002/mana.202300370\">10.1002/mana.202300370</a>.","ama":"Brennecken D. Dunkl convolution and elliptic regularity for Dunkl operators. <i>Mathematische Nachrichten</i>. Published online 2024. doi:<a href=\"https://doi.org/10.1002/mana.202300370\">10.1002/mana.202300370</a>","apa":"Brennecken, D. (2024). Dunkl convolution and elliptic regularity for Dunkl operators. <i>Mathematische Nachrichten</i>. <a href=\"https://doi.org/10.1002/mana.202300370\">https://doi.org/10.1002/mana.202300370</a>","bibtex":"@article{Brennecken_2024, title={Dunkl convolution and elliptic regularity for Dunkl operators}, DOI={<a href=\"https://doi.org/10.1002/mana.202300370\">10.1002/mana.202300370</a>}, journal={Mathematische Nachrichten}, publisher={Wiley}, author={Brennecken, Dominik}, year={2024} }","short":"D. Brennecken, Mathematische Nachrichten (2024).","mla":"Brennecken, Dominik. “Dunkl Convolution and Elliptic Regularity for Dunkl Operators.” <i>Mathematische Nachrichten</i>, Wiley, 2024, doi:<a href=\"https://doi.org/10.1002/mana.202300370\">10.1002/mana.202300370</a>."},"year":"2024"}]