---
_id: '66550'
abstract:
- lang: eng
  text: For an arbitrary reduced root system, we give upper bounds for the Dunkl kernel
    with regular spectral parameter and its derivatives, which are uniform in the
    spatial variable. These estimates generalize well-known sharp upper bounds for
    classical one-variable Bessel functions and for spherical functions of Cartan
    motion groups. As a consequence, we prove that the representing measure of Dunkl's
    intertwining operator is absolutely continuous with respect to the Lebesgue measure
    for multiplicities $k> 1/2$ and generic spectral parameter. This settles a conjecture
    posed in [RdJ02] at least for $k>1/2$.
author:
- first_name: Lukas
  full_name: Langen, Lukas
  id: '73664'
  last_name: Langen
citation:
  ama: Langen L. Uniform bounds on the Dunkl kernel. <i>arXiv:260702176</i>. Published
    online 2026.
  apa: Langen, L. (2026). Uniform bounds on the Dunkl kernel. In <i>arXiv:2607.02176</i>.
  bibtex: '@article{Langen_2026, title={Uniform bounds on the Dunkl kernel}, journal={arXiv:2607.02176},
    author={Langen, Lukas}, year={2026} }'
  chicago: Langen, Lukas. “Uniform Bounds on the Dunkl Kernel.” <i>ArXiv:2607.02176</i>,
    2026.
  ieee: L. Langen, “Uniform bounds on the Dunkl kernel,” <i>arXiv:2607.02176</i>.
    2026.
  mla: Langen, Lukas. “Uniform Bounds on the Dunkl Kernel.” <i>ArXiv:2607.02176</i>,
    2026.
  short: L. Langen, ArXiv:2607.02176 (2026).
date_created: 2026-07-21T13:08:08Z
date_updated: 2026-07-21T13:11:05Z
external_id:
  arxiv:
  - '2607.02176'
language:
- iso: eng
page: '31'
publication: arXiv:2607.02176
status: public
title: Uniform bounds on the Dunkl kernel
type: preprint
user_id: '73664'
year: '2026'
...