Asymptotic behavior of the convolution transform

Abstract

Carmichael and Pathak [1] have given abelian theorems for the H-transform of classical functions and generalized functions as the complex variable of the transform approaches zero or infinity in a wedge domain in the right half plane. Many classical integral transforms are special cases of H-transform. The convolution transform studied by Hirschman and Widder [3] is not a special case of the H-transform. In fact Tanno [4] has shown that certain generalized convolution transform includes the H-transform as a special case. In this paper Abelian theorems for the convolution transform are obtained. In obtaining these results we follow closely Zemanian [5] and Carmichael and Pathak [1]. © 1993, Taylor & Francis Group, LLC. All rights reserved.