T. Vdovenko

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Articles: 2

On extensions of linear functionals with applications to non-symmetrically singular perturbations

Mykola Dudkin, Tetiana Vdovenko

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 24 (2018), no. 3, 193-206

The article is devoted to extensions of linear functionals, generated by scalar products, in a scale of Hilbert spaces. Such extensions are used to consider non-symmetrically singular rank one perturbations of ${\mathcal H}_{-2}$-class. For comparison, we give main definitions and descriptions of singular non-symmetric perturbations of ${\mathcal H}_{-1}$ and ${\mathcal H}_{-2}$-classes.

On nonsymmetric rank one singular perturbations of selfadjoint operators

Mykola Dudkin, Tetiana Vdovenko

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 22 (2016), no. 2, 137-151

We consider nonsymmetric rank one singular perturbations of a selfadjoint operator, i.e., an expression of the form $\tilde A=A+\alpha\left\langle\cdot,\omega_1\right\rangle\omega_2$, $\omega_1\not=\omega_2$, $\alpha\in{\mathbb C}$, in a general case $\omega_1,\omega_2\in{\mathcal H}_{-2}$. 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.


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