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Cauchy and Poisson integral representations for ultradistributions of compact support and distributional boundary values

Published online by Cambridge University Press:  14 November 2011

R. S. Pathak
R. S. Pathak
Affiliation:
Department of Mathematics, Banaras Hindu University, Varanasi 221005, India
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Synopsis

Ultradistributions of compact support are represented as the boundary values of Cauchy and Poisson integrals corresponding to tubular radial domains Tc' =ℝn + iC', C'⊂⊂C, where C is an open, connected, convex cone. The Cauchy integral of is shown to be an analytic function in TC' which satisfies a certain boundedness condition. Analytic functions which satisfy a specified growth condition in TC' have a distributional boundary value which can be used to determine an distribution.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 91 , Issue 1-2 , 1981 , pp. 49 - 62
Copyright
Copyright © Royal Society of Edinburgh 1981

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