# Dual pair of eigenvalues in rank one singular nonsymmetric perturbations

Author
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. Kreins 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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