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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.