M. G. Volkova

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Articles: 5

On one class of nonselfadjoint operators with a discrete spectrum

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

↓ Abstract   |   Article (.pdf)

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

G. M. Gubreev, M. G. Volkova

↓ Abstract   |   Article (.pdf)

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].

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

G. M. Gubreev, M. G. Volkova

↓ Abstract   |   Article (.pdf)

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 one class of Hilbert space uncoditional bases

A. A. Tarasenko, M. G. Volkova

↓ Abstract   |   Article (.pdf)

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 $\mathfrak{H}$.

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

G. M. Gubreev, M. G. Volkova

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


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