The first order asymptotics of the extreme eigenvectors of certain hermitian toeplitz matrices

A. Böttcher; S. Grudsky; E. A. Maksimenko; J. Unterberger

doi:10.1007/s00020-008-1646-x

The first order asymptotics of the extreme eigenvectors of certain hermitian toeplitz matrices

A. Böttcher, S. Grudsky, E. A. Maksimenko, J. Unterberger

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

12 Scopus citations

Abstract

The paper is concerned with Hermitian Toeplitz matrices generated by a class of unbounded symbols that emerge in several applications. The main result gives the third order asymptotics of the extreme eigenvalues and the first order asymptotics of the extreme eigenvectors of the matrices as their dimension increases to infinity.

Original language	English
Pages (from-to)	165-180
Number of pages	16
Journal	Integral Equations and Operator Theory
Volume	63
Issue number	2
DOIs	https://doi.org/10.1007/s00020-008-1646-x
State	Published - Feb 2009
Externally published	Yes

Keywords

Eigenvalue, eigenvector
Fisher-Hartwig symbol
Toeplitz matrix

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10.1007/s00020-008-1646-x

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title = "The first order asymptotics of the extreme eigenvectors of certain hermitian toeplitz matrices",

abstract = "The paper is concerned with Hermitian Toeplitz matrices generated by a class of unbounded symbols that emerge in several applications. The main result gives the third order asymptotics of the extreme eigenvalues and the first order asymptotics of the extreme eigenvectors of the matrices as their dimension increases to infinity.",

keywords = "Eigenvalue, eigenvector, Fisher-Hartwig symbol, Toeplitz matrix",

author = "A. B{\"o}ttcher and S. Grudsky and Maksimenko, {E. A.} and J. Unterberger",

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AU - Böttcher, A.

AU - Grudsky, S.

AU - Maksimenko, E. A.

AU - Unterberger, J.

N1 - Funding Information: This work was partially supported by CONACYT projects 60160 and 80504, Mexico.

PY - 2009/2

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N2 - The paper is concerned with Hermitian Toeplitz matrices generated by a class of unbounded symbols that emerge in several applications. The main result gives the third order asymptotics of the extreme eigenvalues and the first order asymptotics of the extreme eigenvectors of the matrices as their dimension increases to infinity.

AB - The paper is concerned with Hermitian Toeplitz matrices generated by a class of unbounded symbols that emerge in several applications. The main result gives the third order asymptotics of the extreme eigenvalues and the first order asymptotics of the extreme eigenvectors of the matrices as their dimension increases to infinity.

KW - Eigenvalue, eigenvector

KW - Fisher-Hartwig symbol

KW - Toeplitz matrix

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U2 - 10.1007/s00020-008-1646-x

DO - 10.1007/s00020-008-1646-x

M3 - Artículo

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VL - 63

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EP - 180

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

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ER -

The first order asymptotics of the extreme eigenvectors of certain hermitian toeplitz matrices

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Keywords

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