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December 2006 A Calculus Scheme for Clifford Distributions
Fred BRACKX, Bram DE KNOCK, Hennie DE SCHEPPER, David EELBODE
Tokyo J. Math. 29(2): 495-513 (December 2006). DOI: 10.3836/tjm/1170348181

Abstract

The aim of the paper is to construct the fundamental solution of an arbitrary complex power of the Dirac operator, these powers being defined as convolution operators with a kernel expressed in terms of specific distributions in Euclidean space. The desired fundamental solution is found, at least formally, in terms of the same families of distributions as those arising in the kernel of the corresponding operator. Clearly, in order to prove these results in a rigorous way, we first have to investigate the definition and properties of both the convolution and the product of arbitrary elements of the families of distributions under consideration, leading to a very attractive pattern of mutual relations between them.

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Fred BRACKX. Bram DE KNOCK. Hennie DE SCHEPPER. David EELBODE. "A Calculus Scheme for Clifford Distributions." Tokyo J. Math. 29 (2) 495 - 513, December 2006. https://doi.org/10.3836/tjm/1170348181

Information

Published: December 2006
First available in Project Euclid: 1 February 2007

zbMATH: 1126.46027
MathSciNet: MR2284986
Digital Object Identifier: 10.3836/tjm/1170348181

Subjects:
Primary: 46F10
Secondary: 30G35‎

Rights: Copyright © 2006 Publication Committee for the Tokyo Journal of Mathematics

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Vol.29 • No. 2 • December 2006
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