Remarks on a proof of the absolute continuity of the representing measures for Dunkl's intertwining operator

Dominik Brennecken; Margit Rösler

Remarks on a proof of the absolute continuity of the representing measures for Dunkl's intertwining operator

Classical Analysis and ODEs 2026-08-11 v1 Representation Theory

Authors: Dominik Brennecken , Margit Rösler

Abstract

In the published paper [T10], K. Trim\`eche presented a proof of the statement that for suitable nonnegative multiplicities and regular arguments, the representing measures of Dunkl's intertwining operator and its dual are absolutely continuous with respect to Lebesgue measure. In this note, we argue that the essential proofs of this paper are not correct.

Keywords

Dunkl's intertwining operator representing measures absolute continuity Lebesgue measure

Cite

@article{arxiv.2608.10821,
  title  = {Remarks on a proof of the absolute continuity of the representing measures for Dunkl's intertwining operator},
  author = {Dominik Brennecken and Margit Rösler},
  journal= {arXiv preprint arXiv:2608.10821},
  year   = {2026}
}