Mercer's Theorem and Fredholm resolvents

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...

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Bibliographic Details
Published in:Bulletin of the Australian Mathematical Society 1974-12, Vol.11 (3), p.373-380
Main Author: Withers, C.S.
Format: Article
Language:English
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Summary: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).
ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972700044002