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Finitely-generated solutions of certain integral equations

Published online by Cambridge University Press:  20 January 2009

D. Porter  and
D. S. G. Stirling
D. Porter
Affiliation:
Mathematics DepartmentThe UniversityPO Box 220Reading RG6 2AX
D. S. G. Stirling
Affiliation:
Mathematics DepartmentThe UniversityPO Box 220Reading RG6 2AX
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Abstract

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Recent work has shown that the solutions of the second-kind integral equation arising from a difference kernel can be expressed in terms of two particular solutions of the equation. This paper establishes analogous results for a wider class of integral operators, which includes the special case of those arising from difference kernels, where the solution of the general case is generated by a finite number of particular cases. The generalisation is achieved by reducing the problem to one of finite rank. Certain non-compact operators, including those arising from Cauchy singular kernels, are amenable to this approach.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 37 , Issue 2 , June 1994 , pp. 325 - 345
Copyright
Copyright © Edinburgh Mathematical Society 1994

References

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