Spectra of a class of non-self-adjoint matrices

E. B. Davies; Michael Levitin

doi:10.1016/j.laa.2014.01.025

Spectra of a class of non-self-adjoint matrices

E. B. Davies, Michael Levitin^*

^*Corresponding author for this work

University of Reading

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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.

Original language	English
Pages (from-to)	55-84
Number of pages	30
Journal	LINEAR ALGEBRA AND ITS APPLICATIONS
Volume	448
DOIs	https://doi.org/10.1016/j.laa.2014.01.025
Publication status	Published - 1 May 2014

Keywords

Linear operator pencils
Spectral theory
Non-self-adjoint operators
Tri-diagonal matrices
Eigenvalue asymptotics
QUADRATIC EIGENVALUE PROBLEM
PENCILS

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10.1016/j.laa.2014.01.025

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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.",

keywords = "Linear operator pencils, Spectral theory, Non-self-adjoint operators, Tri-diagonal matrices, Eigenvalue asymptotics, QUADRATIC EIGENVALUE PROBLEM, PENCILS",

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AU - Levitin, Michael

PY - 2014/5/1

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N2 - 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.

AB - 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.

KW - Linear operator pencils

KW - Spectral theory

KW - Non-self-adjoint operators

KW - Tri-diagonal matrices

KW - Eigenvalue asymptotics

KW - QUADRATIC EIGENVALUE PROBLEM

KW - PENCILS

U2 - 10.1016/j.laa.2014.01.025

DO - 10.1016/j.laa.2014.01.025

M3 - Article

SN - 0024-3795

VL - 448

SP - 55

EP - 84

JO - LINEAR ALGEBRA AND ITS APPLICATIONS

JF - LINEAR ALGEBRA AND ITS APPLICATIONS

ER -

Spectra of a class of non-self-adjoint matrices

Abstract

Keywords

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