Elementary linear algebra for advanced spectral problems

Johannes Sjöstrand[1]; Maciej Zworski[2]

  • [1] École Polytechnique Centre de Mathématiques Laurent Schwartz UMR 7460, CNRS 91128 Palaiseau (France)
  • [2] University of California Mathematics Department Evans Hall Berkeley, CA 94720 (USA)

Annales de l’institut Fourier (2007)

  • Volume: 57, Issue: 7, page 2095-2141
  • ISSN: 0373-0956

Abstract

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We describe a simple linear algebra idea which has been used in different branches of mathematics such as bifurcation theory, partial differential equations and numerical analysis. Under the name of the Schur complement method it is one of the standard tools of applied linear algebra. In PDE and spectral analysis it is sometimes called the Grushin problem method, and here we concentrate on its uses in the study of infinite dimensional problems, coming from partial differential operators of mathematical physics.

How to cite

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Sjöstrand, Johannes, and Zworski, Maciej. "Elementary linear algebra for advanced spectral problems." Annales de l’institut Fourier 57.7 (2007): 2095-2141. <http://eudml.org/doc/10292>.

@article{Sjöstrand2007,
abstract = {We describe a simple linear algebra idea which has been used in different branches of mathematics such as bifurcation theory, partial differential equations and numerical analysis. Under the name of the Schur complement method it is one of the standard tools of applied linear algebra. In PDE and spectral analysis it is sometimes called the Grushin problem method, and here we concentrate on its uses in the study of infinite dimensional problems, coming from partial differential operators of mathematical physics.},
affiliation = {École Polytechnique Centre de Mathématiques Laurent Schwartz UMR 7460, CNRS 91128 Palaiseau (France); University of California Mathematics Department Evans Hall Berkeley, CA 94720 (USA)},
author = {Sjöstrand, Johannes, Zworski, Maciej},
journal = {Annales de l’institut Fourier},
keywords = {Grushin problem; Schur complement; Feshbach reduction; eigenvalues; resonances; trace formulæ; feshback reduction; trace formulae; Poisson summation formula},
language = {eng},
number = {7},
pages = {2095-2141},
publisher = {Association des Annales de l’institut Fourier},
title = {Elementary linear algebra for advanced spectral problems},
url = {http://eudml.org/doc/10292},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Sjöstrand, Johannes
AU - Zworski, Maciej
TI - Elementary linear algebra for advanced spectral problems
JO - Annales de l’institut Fourier
PY - 2007
PB - Association des Annales de l’institut Fourier
VL - 57
IS - 7
SP - 2095
EP - 2141
AB - We describe a simple linear algebra idea which has been used in different branches of mathematics such as bifurcation theory, partial differential equations and numerical analysis. Under the name of the Schur complement method it is one of the standard tools of applied linear algebra. In PDE and spectral analysis it is sometimes called the Grushin problem method, and here we concentrate on its uses in the study of infinite dimensional problems, coming from partial differential operators of mathematical physics.
LA - eng
KW - Grushin problem; Schur complement; Feshbach reduction; eigenvalues; resonances; trace formulæ; feshback reduction; trace formulae; Poisson summation formula
UR - http://eudml.org/doc/10292
ER -

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Citations in EuDML Documents

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  1. Johannes Sjöstrand, Eigenvalue distribution for non-self-adjoint operators with small multiplicative random perturbations
  2. Johannes Sjöstrand, Weyl asymptotics for non-self-adjoint operators with small multiplicative random perturbations
  3. Michael Hitrik, Karel Pravda-Starov, Eigenvalues and subelliptic estimates for non-selfadjoint semiclassical operators with double characteristics
  4. Johannes Sjöstrand, Eigenvalue distribution for non-self-adjoint operators on compact manifolds with small multiplicative random perturbations
  5. Stéphane Nonnenmacher, Quantum transfer operators and quantum scattering
  6. Johannes Sjöstrand, Spectral properties of non-self-adjoint operators

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