Persistence of embedded eigenvalues

Research output: Contribution to journalArticle

Abstract

We consider conditions under which an embedded eigenvalue of a self-adjoint operator remains embedded under small perturbations. In the case of a simple eigenvalue embedded in continuous spectrum of multiplicity m<∞m<∞ we show that in favorable situations, the set of small perturbations of a suitable Banach space which do not remove the eigenvalue form a smooth submanifold of codimension m. We also have results regarding the cases when the eigenvalue is degenerate or when the multiplicity of the continuous spectrum is infinite.

Details

Authors
Organisations
External organisations
  • Hebrew University of Jerusalem
  • University of Virginia
  • Stockholm University
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematical Analysis

Keywords

  • embedded eigenvalues, perturbation
Original languageEnglish
Pages (from-to)451-477
Number of pages27
JournalJournal of Functional Analysis
Volume261
Issue number2
Publication statusPublished - 2011
Publication categoryResearch
Peer-reviewedYes