Variational principles for eigenvalues of block operator matrices

H. Langer, M. Langer, Christiane Tretter

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

In this paper variational principles for block operator matrices are established which are based on functionals associated with the quadratic numerical range. These principles allow to characterize, e.g., eigenvalues in gaps of the essential spectrum and to derive two-sided eigenvalue estimates in terms of the spectral characteristics of the entries of the block operator matrix. The results are applied to a second order partial differential equation depending on the spectral parameter nonlinearly.
LanguageEnglish
Pages1427-1460
Number of pages34
JournalIndiana University Mathematics Journal
Volume51
Issue number6
DOIs
Publication statusPublished - 2002

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Operator Matrix
Block Matrix
Variational Principle
Eigenvalue Estimates
Eigenvalue
Numerical Range
Essential Spectrum
Second order differential equation
Partial differential equation

Keywords

  • Eigenvalues
  • block operator matrix

Cite this

Langer, H. ; Langer, M. ; Tretter, Christiane. / Variational principles for eigenvalues of block operator matrices. In: Indiana University Mathematics Journal. 2002 ; Vol. 51, No. 6. pp. 1427-1460.
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Variational principles for eigenvalues of block operator matrices. / Langer, H.; Langer, M.; Tretter, Christiane.

In: Indiana University Mathematics Journal, Vol. 51, No. 6, 2002, p. 1427-1460.

Research output: Contribution to journalArticle

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AU - Langer, H.

AU - Langer, M.

AU - Tretter, Christiane

PY - 2002

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AB - In this paper variational principles for block operator matrices are established which are based on functionals associated with the quadratic numerical range. These principles allow to characterize, e.g., eigenvalues in gaps of the essential spectrum and to derive two-sided eigenvalue estimates in terms of the spectral characteristics of the entries of the block operator matrix. The results are applied to a second order partial differential equation depending on the spectral parameter nonlinearly.

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KW - block operator matrix

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