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The Hankel transform of some classes of generalized functions and connections with fractional integration*†

Published online by Cambridge University Press:  14 November 2011

Adam C. McBride
Adam C. McBride
Affiliation:
Department of Mathematics, University of Strathclyde
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Synopsis

In previous papers [11,12,13], certain spaces of generalized functions were studied from the point of view of fractional calculus. In this paper, we show how a Hankel transform Hv of order v can be defined on for all complex numbers v except for those lying on a countable number of lines of the form Re v = constant in the complex v-plane. The mapping properties of Hv on are obtained. Various connections between Hv (or modifications of Hv) and operators of fractional integration are examined.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 81 , Issue 1-2 , 1978 , pp. 95 - 117
Copyright
Copyright © Royal Society of Edinburgh 1978

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