Mercer's Theorem and Fredholm resolvents

Source abstract

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 R p 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 ).