Mykola Dudkin

On nonsymmetric rank one singular perturbations of selfadjoint operators

We consider nonsymmetric rank one singular perturbations of a selfadjoint operator, i.e., an expression of the form $\tilde A = A + α\left\langle\cdot, ω_1\right\rangleω_2$, $ω_1\not = ω_2$, $α\in{\mathbb C}$, in a general case $ω_1,ω_2\in{\mathcal H}_{-2}$. Using a constructive description of the perturbed operator $\tilde A$, we investigate some spectral and approximations properties of $\tilde A$. The wave operators corresponding to the couple $A$, $\tilde A$ and a series of examples are also presented.