Inversion Formulas for the Dunkl Intertwining Operator and Its Dual on Spaces of Functions and Distributions

Khalifa Trimèche

doi:10.3842/SIGMA.2008.067

Inversion Formulas for the Dunkl Intertwining Operator and Its Dual on Spaces of Functions and Distributions

Classical Analysis and ODEs 2008-09-30 v1 Functional Analysis

Authors: Khalifa Trimèche

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Abstract

In this paper we prove inversion formulas for the Dunkl intertwining operator $V_k$ and for its dual ${}^tV_k$ and we deduce the expression of the representing distributions of the inverse operators $V_k^{-1}$ and ${}^tV_k^{-1}$ , and we give some applications.

Keywords

dunkl intertwining operator inversion formulas distributions representation harmonic analysis

Cite

@article{arxiv.0809.5021,
  title  = {Inversion Formulas for the Dunkl Intertwining Operator and Its Dual on Spaces of Functions and Distributions},
  author = {Khalifa Trimèche},
  journal= {arXiv preprint arXiv:0809.5021},
  year   = {2008}
}

Comments

This is a contribution to the Special Issue on Dunkl Operators and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

Inversion Formulas for the Dunkl Intertwining Operator and Its Dual on Spaces of Functions and Distributions

Abstract

Keywords

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