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Spectra of a class of non-self-adjoint matrices

By E. Brian Davies and Michael Levitin

Abstract

We consider a new class of non-self-adjoint matrices that arise from an indefinite self- adjoint linear pencil of matrices, and obtain the spectral asymptotics of the spectra as the size of the matrices diverges to infinity. We prove that the spectrum is qualitatively different when a certain parameter c equals 0, and when it is non-zero, and that certain features of the spectrum depend on Diophantine properties of c

Publisher: Elsevier
Year: 2014
OAI identifier: oai:centaur.reading.ac.uk:35789

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