On the eigenvalues and eigenfunctions of some integral operators

Some properties of the eigenvalues of the integral operator Kgt defined as Kτf(x) = ∫0τK(x − y) f (y) dy were studied by [1.], 554–566), with some assumptions on the kernel K(x). In this paper the eigenfunctions of the operator Kτ are shown to be continuous functions of τ under certain circumstances. Also, the results of Vittal Rao and the continuity of eigenfunctions are shown to hold for a larger class of kernels.