Non-self-adjoint harmonic oscillator, compact semigroups and pseudospectra

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28 Citations (Scopus)

Abstract

We provide new information concerning the pseudospectra of the complex harmonic oscillator. Our analysis illustrates two different techniques for getting resolvent norm estimates. The first uses the JWKB method and extends for this particular potential some results obtained recently by E.B. Davies. The second relies on the fact that the bounded holomorphic semigroup generated by the complex harmonic oscillator is of Hilbert-Schmidt type in a maximal angular region. In order to show this last property, we deduce a non-self-adjoint version of the classical Mehler's formula.

Original languageEnglish
Pages (from-to)413-429
Number of pages17
JournalJournal of Operator Theory
Volume47
Issue number2
Publication statusPublished - 1 Mar 2002

Keywords

  • Bounded holomorphic semigroups
  • Complex harmonic oscillator
  • JWKB method
  • Mehler's formula
  • Non-self-adjoint
  • Pseudospectrum
  • Resolvent norm estimates

ASJC Scopus subject areas

  • Algebra and Number Theory

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