Work

Dunkl convolution and elliptic regularity for Dunkl operators

Year: 2024

Type: article

Abstract: 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.

Source: Mathematische Nachrichten

DOI: 10.1002/mana.202300370

Author: Dominik Brennecken

Institution: Paderborn University

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,300

Funder: Deutsche Forschungsgemeinschaft