Nonself-adjoint operators with almost Hermitian spectrum: Matrix model. I

Alexander V. Kiselev, Serguei N. Naboko

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8 Citations (SciVal)

Abstract

Nonself-adjoint, nondissipative perturbations of bounded self-adjoint operators with real purely singular spectrum are considered. Using a functional model of a nonself-adjoint operator as a principal tool, spectral properties of such operators are investigated. In particular, in the case of rank two perturbations the pure point spectral component is completely characterized in terms of matrix elements of the operators' characteristic function.

Original languageEnglish
Pages (from-to)115-130
Number of pages16
JournalJournal of Computational and Applied Mathematics
Volume194
Issue number1 SPEC. ISS.
DOIs
Publication statusPublished - 15 Sept 2006

Bibliographical note

Funding Information:
The authors acknowledge support received from RFBR (Grant No. 03-01-00090) and IRCSET. They also express their deep gratitude to the referee of this paper for making a number of extremely helpful comments.

Keywords

  • Almost Hermitian spectrum
  • Functional model
  • Matrix model
  • Pure point spectrum

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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