TY  - JOUR
ID  - Behrndt2016
LB  - Behrndt2016
AU  - Behrndt, Jussi
AU  - Möws, Roland
AU  - Trunk, Carsten
TI  - Eigenvalue estimates for operators with finitely many negative squares
ST  - Eigenvalue estimates for operators with finitely many negative squares
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2016
VL  - 36
IS  - 6
SP  - 717
EP  - 734
DO  - http://dx.doi.org/10.7494/OpMath.2016.36.6.717
UR  - http://dx.doi.org/10.7494/OpMath.2016.36.6.717
AB  - 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.
KW  - selfadjoint operator
KW  - Krein space
KW  - finitely many negative squares
KW  - eigenvalue estimate
KW  - indefinite Sturm-Liouville operator
SN  - 1232-9274
ER  -