Dual pair of eigenvalues in rank one singular nonsymmetric perturbations

T. I. Vdovenko, M. E. Dudkin
National Technical University of Ukraine, Kyiv, Ukraine
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.
rank one singular perturbation; eigenvalue problem; M. Krein’s formula; nonselfadjoint perturbation; deviating argument
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