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Asymptotic behaviour of the H-transform in the complex domain

Published online by Cambridge University Press:  24 October 2008

Richard D. Carmichael  and
Ram S. Pathak
Richard D. Carmichael
Affiliation:
Wake Forest University, Winston-Salem, NC 27109, U.S.A.
Ram S. Pathak
Affiliation:
Banaras Hindu University, Varanasi 221005, India
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Abstract

Abelian theorems for the H-transform of functions and generalized functions are obtained as the complex variable of the transform approaches zero or infinity in a wedge domain in the right half plane. Quasi-asymptotic behaviour (q.a.b.) of the H-transformable generalized functions is defined. A structure theorem for generalized functions possessing q.a.b. is proved and is applied to obtain the asymptotic behaviour of the H-transform of generalized functions having q.a.b. The theorems are illustrated by examples.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 102 , Issue 3 , November 1987 , pp. 533 - 552
Copyright
Copyright © Cambridge Philosophical Society 1987

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