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Analytic functions having distributional boundary values in W′-spaces

Published online by Cambridge University Press:  24 October 2008

R. S. Pathak
R. S. Pathak
Affiliation:
Banaras Hindu University, Varanasi 221005, India
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Abstract

It is shown that the functions which are analytic in tubular radial domains and satisfy certain growth conditions have distributional boundary values in the weak topology of (WΩ)′-space. Representation of analytic functions in terms of distributional boundary values are given. Converse results are also obtained. An analytic decomposition theorem is proved. The main theorems are established by means of a number of lemmas concerning WM, WΩ spaces and their dual spaces. Several new lemmas are proved for K{Mp} spaces from which results for WM-spaces can be easily deduced.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 87 , Issue 2 , March 1980 , pp. 227 - 242
Copyright
Copyright © Cambridge Philosophical Society 1980

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