JournalsjstVol. 2, No. 4pp. 329–354

Generalized Weyl theorems and spectral pollution in the Galerkin method

  • Lyonell Boulton

    Heriot-Watt University, Edinburgh, UK
  • Nabile Boussaïd

    Université de Franche-Comté, Besançon, France
  • Mathieu Lewin

    Université de Cergy-Pontoise, France
Generalized Weyl theorems and spectral pollution in the Galerkin method cover
Download PDF

Abstract

We consider a general framework for investigating spectral pollution in the Galerkin method. We show how this phenomenon is characterised via the existence of particular Weyl sequences which are singular in a suitable sense. For a given semi-bounded selfadjoint operator A, we identify relative compactness conditions on a selfadjoint perturbation B, ensuring that the limiting set of spectral pollution of A and B coincide. Our results show that, under perturbation, this limiting set behaves in a similar fashion as the essential spectrum.

Cite this article

Lyonell Boulton, Nabile Boussaïd, Mathieu Lewin, Generalized Weyl theorems and spectral pollution in the Galerkin method. J. Spectr. Theory 2 (2012), no. 4, pp. 329–354

DOI 10.4171/JST/32