Methods and Applications of Analysis

Volume 14 (2007)

Number 4

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

Pages: 387 – 404

DOI: http://dx.doi.org/10.4310/MAA.2007.v14.n4.a5

Authors

Slaim Ben Farah

Kamel Mokni

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.

Keywords

Dunkl-convolution; tempered distributions; hypoelliptic equations

2010 Mathematics Subject Classification

42A38, 42A85, 46F10

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