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Solution of dual integral equations of Titchmarsh type using generalised functions*

Published online by Cambridge University Press:  14 November 2011

Adam C. McBride
Adam C. McBride
Affiliation:
University of Strathclyde, Glasgow
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Synopsis

The theories of fractional calculus and of the Hankel transform developed in for the spaces F′p, μ of generalised functions are used to study distributional analogues of dual integral equations of Titchmarsh type. These are shown to have infinitely many solutions in F′p, μ under very general conditions on the parameters involved. These results are used to study the corresponding classical problem in weighted Lp spaces. Existence and uniqueness of classical solutions are investigated and examples given of both uniqueness and non-uniqueness for the classical problem.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 83 , Issue 3-4 , 1979 , pp. 263 - 281
Copyright
Copyright © Royal Society of Edinburgh 1979

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