Generalised Weyl theorems and spectral pollution in the Galerkin method

Lyonell Boulton, Nabile Boussaïd, Mathieu Lewin

Research output: Contribution to journalArticle

10 Citations (Scopus)

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 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.

Original languageEnglish
Pages (from-to)329-354
Number of pages26
JournalJournal of Spectral Theory
Volume2
Issue number4
DOIs
Publication statusPublished - 2012

Keywords

  • Galerkin method
  • Generalised essential spectrum
  • Spectral pollution
  • Weyl's Theorem

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Geometry and Topology

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