# A. A. Tarasenko

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Articles: 6

### On one class of nonselfadjoint operators with a discrete spectrum

Methods Funct. Anal. Topology 17 (2011), no. 3, 211-218

In this work completely continious nondissipative operators with two-dimensional imaginary parts, acting in separable Hilbert space are studied. The criteria of completeness and unconditional basis property of root vectors of such operators are obtained. The results are formulated in terms of characteristic matrix-valued functions of nonselfadjoint operators and proved using analysis of functional models in de Branges spaces.

### About one class of Hilbert space uncoditional bases

Methods Funct. Anal. Topology 13 (2007), no. 3, 296-300

Let a sequence $\left\{v_k \right\}^{+\infty}_{-\infty}\in l_2$ and a real sequence $\left\{\lambda_k \right\}^{+\infty}_{-\infty}$ such that $\left\{\lambda_k^{-1} \right\}^{+\infty}_{-\infty}\in l_2$, and an orthonormal basis $\left\{e_k \right\}^{+\infty}_{-\infty}$ of a Hilbert space be given. We describe a sequence $M=\left\{\mu_k \right\}^{+\infty}_{-\infty}$, $M\cap \mathbb{R}=\varnothing$, such that the families $$f_k = \sum\limits_{j\in\mathbb{Z}} {v_j\left(\lambda_j-\bar{\mu}_k \right)^{-1}}e_k, \quad k\in \mathbb{Z}$$ form an unconditional basis in $\mathfrak{H}$.

### About one interpolation problem by entire functions of exponential type in the weight spaces

Methods Funct. Anal. Topology 11 (2005), no. 4, 370-375

### On a class of finite-dimensional perturbations of dissipative Volterra operators

Methods Funct. Anal. Topology 11 (2005), no. 1, 65-72

### On a class of generators of one-parameter $C_{0}$-semigroup of operators

Methods Funct. Anal. Topology 9 (2003), no. 2, 179-184

### Unconditional basis property for some families of functions and continuous invertibility of Toeplitz operators with unimodular symbols

Methods Funct. Anal. Topology 8 (2002), no. 1, 30-35