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, 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

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