Opuscula Math. 36, no. 6 (2016), 717-734
http://dx.doi.org/10.7494/OpMath.2016.36.6.717

 
Opuscula Mathematica

Eigenvalue estimates for operators with finitely many negative squares

Jussi Behrndt
Roland Möws
Carsten Trunk

Abstract. Let \(A\) and \(B\) be selfadjoint operators in a Krein space. Assume that the resolvent difference of \(A\) and \(B\) is of rank one and that the spectrum of \(A\) consists in some interval \(I\subset\mathbb{R}\) of isolated eigenvalues only. In the case that \(A\) is an operator with finitely many negative squares we prove sharp estimates on the number of eigenvalues of \(B\) in the interval \(I\). The general results are applied to singular indefinite Sturm-Liouville problems.

Keywords: selfadjoint operator, Krein space, finitely many negative squares, eigenvalue estimate, indefinite Sturm-Liouville operator.

Mathematics Subject Classification: 47A55, 47B50.

Full text (pdf)

  • Jussi Behrndt
  • Technische Universität Graz, Institut für Numerische Mathematik, Steyrergasse 30, 8010 Graz, Austria
  • Roland Möws
  • Krossener Str. 17, D-10245 Berlin, Germany
  • Carsten Trunk
  • Technische Universität Ilmenau, Institut für Mathematik, Postfach 100565, D-98684 Ilmenau, Germany
  • Communicated by A. Shkalikov.
  • Received: 2016-04-16.
  • Revised: 2016-05-24.
  • Accepted: 2016-05-24.
  • Published online: 2016-10-29.
Opuscula Mathematica - cover

Cite this article as:
Jussi Behrndt, Roland Möws, Carsten Trunk, Eigenvalue estimates for operators with finitely many negative squares, Opuscula Math. 36, no. 6 (2016), 717-734, http://dx.doi.org/10.7494/OpMath.2016.36.6.717

Download this article's citation as:
a .bib file (BibTeX),
a .ris file (RefMan),
a .enw file (EndNote)
or export to RefWorks.

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.