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Mercer's Theorem and Fredholm resolvents

Published online by Cambridge University Press:  17 April 2009

C.S. Withers
C.S. Withers
Affiliation:
Applied Mathematics Division, Department of Scientific and Industrial Research, Wellington, New Zealand.
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Abstract

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Multivariate versions of Mercer's Theorem and the usual expansions of the resolvent and Fredholm determinant are shown to hold for an n × n symmetric kernel N(x, y) with arbitrary domain in Rp under weakened continuity conditions. Further, the resolvent and determinant of N(x, y) − a(x)b(y) are given in terms of those of N(x, y).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 11 , Issue 3 , December 1974 , pp. 373 - 380
Copyright
Copyright © Australian Mathematical Society 1974

References

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