# G. M. Gubreev

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

G. M. Gubreev, M. G. Volkova, A. A. Tarasenko

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.

### Unconditional bases of de Branges spaces and interpolation problems corresponding to them

Methods Funct. Anal. Topology **17** (2011), no. 2, 144-149

In this paper the unconditional bases of de Branges spaces are constructed from the values of reproducing kernels. Appropriate problems of interpolation by entire functions are also considered. The paper is a continuation of papers [2, 3].

### A spectral decomposition in one class of non-selfadjoint operators

G. M. Gubreev, M. V. Dolgopolova, S. I. Nedobachiy

Methods Funct. Anal. Topology **16** (2010), no. 2, 140-157

In this paper, a class of special finite dimensional perturbations of Volterra operators in Hilbert spaces is investigated. The main result of the article is finding necessary and sufficient conditions for an operator in a chosen class to be similar to the orthogonal sum of a dissipative and an anti-dissipative operators with finite dimensional imaginary parts.

### One remark about the unconditional exponential bases and cosine bases, connected with them

Methods Funct. Anal. Topology **14** (2008), no. 4, 330-333

In the paper we consider examples of basis families $\{\cos \lambda_k t\}^\infty_1$, $\lambda_k>0$, in the space $L_2(0,\sigma)$, such that systems $\{e^{i\lambda_kt},e^{-i\lambda_kt}\}^\infty_1$ don't form an unconditional basis in space $L_2(-\sigma,\sigma)$.

### About nilpotent $C_0$-semigroups of operators in the Hilbert spaces and criteria for similarity to the integration operator

G. V. Lukashenko, G. M. Gubreev

Methods Funct. Anal. Topology **14** (2008), no. 1, 60-66

In the paper, we describe a class of operators $A$ that have empty spectrum and satisfy the nilpotency property of the generated $C_0$-semigroup $U(t)=\exp\{-iAt\},\, t\geqslant 0$, and such that the operator$A^{-1}$ is similar to the integration operator on the corresponding space $L_2(0,a)$.

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

G. M. Gubreev, A. A. Tarasenko

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

### Damir Zyamovich Arov (to the 70th anniversary of his birth)

V. M. Adamyan, Yu. M. Berezansky, M. L. Gorbachuk, V. I. Gorbachuk, G. M. Gubreev, A. N. Kochubei, M. M. Malamud

Methods Funct. Anal. Topology **10** (2004), no. 2, 1-3

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

G. M. Gubreev, A. A. Tarasenko

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

### On a class of unconditional bases in the weighted spaces of the entire functions whose order of growth is equal to 1/2 and on their applications

Methods Funct. Anal. Topology **7** (2001), no. 3, 22-32