An initial-value method for integral operators V. Kernels depending upon a parameter

摘要

A new technique is presented for the calculation of the eigenvalues and eigenfunctions of integral operators where the kernel is an entire function of the eigenvalue parameter. The method combines a number of results from functions of a complex variable and integral equations with a new technique for converting Fredholm integral equations into an initial-value system of ordinary differential equations. Several pertinent examples are presented which illustrate the efficacy of the procedure.