Spectral theory of large Wiener–Hopf operators with complex-symmetric kernels and rational symbols

Abstract

AbstractThis paper is devoted to the asymptotic behaviour of individual eigenvalues of truncated Wiener–Hopf integral operators over increasing intervals. The kernel of the operators is complex-symmetric and has a rational Fourier transform. Under additional hypotheses, the main result describes the location of the eigenvalues and provides their asymptotic expansions in terms of the reciprocal of the length of the truncation interval. Also determined is the structure of the eigenfunctions.