Local spectral deformation

Matthias Engelmann, Jacob Schach Møller, Morten Grud Rasmussen

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Abstract

We develop an analytic perturbation theory for eigenvalues with finite multiplicities, embedded into the essential spectrum of a self-adjoint operator H. We assume the existence of another self-adjoint operator A for which the family H θ = eiθAHe -iθA extends analytically from the real line to a strip in the complex plane. Assuming a Mourre estimate holds for i[H, A] in the vicinity of the eigenvalue, we prove that the essential spectrum is locally deformed away from the eigenvalue, leaving it isolated and thus permitting an application of Kato's analytic perturbation theory.

Original languageEnglish
JournalAnnales de l'Institut Fourier
Volume68
Issue number2
Pages (from-to)767-804
Number of pages38
ISSN0373-0956
Publication statusPublished - 2018

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Keywords

  • Analytic perturbation theory
  • Mourre theory
  • Spectral deformation

Cite this

Engelmann, M., Møller, J. S., & Rasmussen, M. G. (2018). Local spectral deformation. Annales de l'Institut Fourier, 68(2), 767-804.