Dual pair of eigenvalues in rank one singular nonsymmetric perturbations

Author
T. I. Vdovenko, M. E. Dudkin
National Technical University of Ukraine, Kyiv, Ukraine
Abstract
In the separable Hilbert space, we discuss the eigenvalue problem for a rank one singular nonselfadjoint perturbation of a selfadjoint operator $A$, by nonsymmetric potential ($\delta_1\not=\delta_2$) in the form $\tilde A=A+\alpha\left\langle\cdot,\delta_1\right\rangle\delta_2$. We give the constructive description of such sort operator $\tilde A$ which possess two new points in the point spectrum in case of weakly singular perturbations.
Keywords
rank one singular perturbation; eigenvalue problem; M. Krein’s formula; nonselfadjoint perturbation; deviating argument
DOI
doi:10.15330/ms.48.2.156-164
Reference
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Pages
156-164
Volume
48
Issue
2
Year
2017
Journal
Matematychni Studii
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