Persistence of embedded eigenvalues

Shmuel Agmon, Ira Herbst, Sara Maad Sasane*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

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< 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.

Original languageEnglish
Pages (from-to)451-477
Number of pages27
JournalJournal of Functional Analysis
Volume261
Issue number2
DOIs
StatePublished - 15 Jul 2011

Keywords

  • Embedded eigenvalues
  • Perturbation

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