Methods and Applications of Analysis

Hypoelliptic convolution equations in $\cal{S}' (\Bbb R)$ for the Dunkl theory on $\Bbb R$

Slaim Ben Farah and Kamel Mokni

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Abstract

The aim of this paper is to characterize hypoelliptic convolution-equations in $\cal{S}' (\Bbb R)$ for the Dunkl theory on the real line. For this we determine the spaces of convolution and multiplication operators in $\cal{S}' (\Bbb R)$ for the Dunkl convolution and we show that the Fourier-Dunkl transform is a topological isomorphism between them.

Article information

Source
Methods Appl. Anal., Volume 14, Number 4 (2007), 387-404.

Dates
First available in Project Euclid: 4 November 2008

Permanent link to this document
https://projecteuclid.org/euclid.maa/1225813983

Mathematical Reviews number (MathSciNet)
MR2467107

Zentralblatt MATH identifier
1182.46027

Subjects
Primary: 46F10: Operations with distributions 42A85: Convolution, factorization 42A38: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type

Keywords
Dunkl-convolution tempered distributions hypoelliptic equations

Citation

Ben Farah, Slaim; Mokni, Kamel. Hypoelliptic convolution equations in $\cal{S}' (\Bbb R)$ for the Dunkl theory on $\Bbb R$. Methods Appl. Anal. 14 (2007), no. 4, 387--404. https://projecteuclid.org/euclid.maa/1225813983


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