Variational principles and eigenvalue estimates for unbounded block operator matrices and applications

Margarita Kraus; M. Langer; Christiane Tretter

doi:10.1016/j.cam.2004.01.024

Variational principles and eigenvalue estimates for unbounded block operator matrices and applications

Margarita Kraus, M. Langer, Christiane Tretter

Mathematics And Statistics

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

20 Citations (Scopus)

Abstract

In this paper we establish variational principles, eigenvalue estimates and asymptotic formulae for eigenvalues of three different classes of unbounded block operator matrices. The results allow to characterise eigenvalues that are not necessarily located at the boundary of the spectrum. Applications to an example from magnetohydrodynamics and to Dirac operators on certain manifolds are given.

Original language	English
Pages (from-to)	311-334
Number of pages	24
Journal	Journal of Computational and Applied Mathematics
Volume	171
Issue number	1-2
DOIs	https://doi.org/10.1016/j.cam.2004.01.024
Publication status	Published - Oct 2004

Keywords

variational principle for eigenvalues
estimates for eigenvalues
asymptotic distribution of eigenvalues
quadratic numerical range
magnetohydrodynamics
warped product of spin manifolds
dirac operator

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10.1016/j.cam.2004.01.024

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title = "Variational principles and eigenvalue estimates for unbounded block operator matrices and applications",

abstract = "In this paper we establish variational principles, eigenvalue estimates and asymptotic formulae for eigenvalues of three different classes of unbounded block operator matrices. The results allow to characterise eigenvalues that are not necessarily located at the boundary of the spectrum. Applications to an example from magnetohydrodynamics and to Dirac operators on certain manifolds are given.",

keywords = "variational principle for eigenvalues, estimates for eigenvalues, asymptotic distribution of eigenvalues, quadratic numerical range, magnetohydrodynamics, warped product of spin manifolds, dirac operator",

author = "Margarita Kraus and M. Langer and Christiane Tretter",

year = "2004",

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T1 - Variational principles and eigenvalue estimates for unbounded block operator matrices and applications

AU - Kraus, Margarita

AU - Langer, M.

AU - Tretter, Christiane

PY - 2004/10

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N2 - In this paper we establish variational principles, eigenvalue estimates and asymptotic formulae for eigenvalues of three different classes of unbounded block operator matrices. The results allow to characterise eigenvalues that are not necessarily located at the boundary of the spectrum. Applications to an example from magnetohydrodynamics and to Dirac operators on certain manifolds are given.

AB - In this paper we establish variational principles, eigenvalue estimates and asymptotic formulae for eigenvalues of three different classes of unbounded block operator matrices. The results allow to characterise eigenvalues that are not necessarily located at the boundary of the spectrum. Applications to an example from magnetohydrodynamics and to Dirac operators on certain manifolds are given.

KW - variational principle for eigenvalues

KW - estimates for eigenvalues

KW - asymptotic distribution of eigenvalues

KW - quadratic numerical range

KW - magnetohydrodynamics

KW - warped product of spin manifolds

KW - dirac operator

U2 - 10.1016/j.cam.2004.01.024

DO - 10.1016/j.cam.2004.01.024

M3 - Article

SN - 0377-0427

VL - 171

SP - 311

EP - 334

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 1-2

ER -

Variational principles and eigenvalue estimates for unbounded block operator matrices and applications

Abstract

Keywords

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