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

Published online by Cambridge University Press:  27 April 2011

ALBRECHT BÖTTCHER ,
SERGEI GRUDSKY  and
ARIEH ISERLES
ALBRECHT BÖTTCHER
Affiliation:
Fakultät für Mathematik, TU Chemnitz, 09107 Chemnitz, Germany. e-mail: albrecht.boettcher@mathematik.tu-chemnitz.de
SERGEI GRUDSKY
Affiliation:
Departamento de Matemáticas, CINVESTAV del I.P.N., Apartado Postal 14-740, 07000 México, D.F., México. e-mail: grudsky@math.cinvestav.mx
ARIEH ISERLES
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB30WA. e-mail: a.iserles@damtp.cam.ac.uk
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Abstract

This 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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 151 , Issue 1 , July 2011 , pp. 161 - 191
Copyright
Copyright © Cambridge Philosophical Society 2011

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