Spherical means, distributions and convolution operators in Clifford analysis
type: Item
instance of: scholarly article
title: Spherical means, distributions and convolution operators in Clifford analysis
zbMATH Open document ID: 1056.30050
DOI: 10.1142/S0252959903000141
published in: Chinese Annals of Mathematics. Series B
publication date: 2004-03-17T00:00:00Z
review text: There are considered Clifford algebra-valued distributions, that is, left or right linear functionals on the spaces of Clifford algebra-valued test functions. In a previous paper the authors introduced three families of distributions which are interrelated by the action (on the left or on the right) of the Dirac operator. For the specific values of the parameters determining those distributions, the latter turns into known kernel functions in harmonic and Clifford analysis, thus illustrating the unifying character of the approach, for instance, one of them reduces to the higher dimensional analog of the ``Principal Value'' distribution on the real line and the kernel for the Hilbert transform; the others two reduce to the fundamental solutions of the Dirac and the Laplace operators, etc. In the paper, the fourth family of distributions is constructed for which threefold motivation is given and its importance for constructing new distributions generalizing the principal value distributions is explained.
reviewed by: M. Shapiro
Mathematics Subject Classification ID: 30G35
Mathematics Subject Classification ID: 46F10
zbMATH DE Number: 2059850
zbMATH Keywords: Clifford analysis
zbMATH Keywords: distributions
zbMATH Keywords: convolution operators
zbMATH Keywords: principal value
author: F. Brackx
author: Richard Delanghe
author: Frank Sommen
MaRDI profile type: Publication
full work available at URL: s0252959903000141
OpenAlex ID: W2223116409
description: scientific article; zbMATH DE number 2059850