11 citations · 55 across the 38 of their papers we have counts for
29 papers · 1 filter
On the multiplication operator by an independent variable in matrix Sobolev spaces
Sergey M. Zagorodnyuk
We study the operator of multiplication by an independent variable in a matrix Sobolev space . In the cases of finite measures on with a…
On the similarity of complex symmetric operators to perturbations of restrictions of normal operators
Sergey M. Zagorodnyuk
In this paper we consider a problem of the similarity of complex symmetric operators to perturbations of restrictions of normal operators. For a subclass of cyclic complex symmetri…
On the truncated multidimensional moment problems in
Sergey M. Zagorodnyuk
We consider the problem of finding a (non-negative) measure on such that $\int_{\mathbb{C}^n} \mathbf{z}^{\mathbf{k}} dμ(\mathbf{z}) = s_{\mathbf{k…
On extensions of commuting tuples of symmetric and isometric operators
Sergey M. Zagorodnyuk
In this paper we study extensions of commuting tuples of symmetric and isometric operators to commuting tuples of self-adjoint and unitary operators. Some conditions which ensure t…
The operator approach to the truncated multidimensional moment problem
Sergey M. Zagorodnyuk
We study the truncated multidimensional moment problem with a general type of truncations. The operator approach to the moment problem is presented. A way to construct atomic solut…
On the truncated two-dimensional moment problem
Sergey M. Zagorodnyuk
We study the truncated two-dimensional moment problem (with rectangular data): to find a non-negative measure , , such that $\int_{\mathbb{R}^…
The Nevanlinna-type parametrization for the operator Hamburger moment problem
Sergey M. Zagorodnyuk
In this paper we obtain a Nevanlinna-type parametrization for the operator Hamburger moment problem. The moment problem is not supposed to be necessarily completely indeterminate.…
Characteristic properties for a generalized resolvent of a pair of commuting isometric operators
Sergey M. Zagorodnyuk
In this paper we consider a notion of a generalized resolvent for a pair of commuting isometric operators in a Hilbert space . Characteristic properties of the generalized resol…
On the truncated operator trigonometric moment problem
Sergey M. Zagorodnyuk
In this paper we study the truncated operator trigonometric moment problem. All solutions of the moment problem are described by a Nevanlinna-type parameterization. In the case of…
A refined polar decomposition for -unitary operators
Sergey M. Zagorodnyuk
In this paper, we shall characterize the components of the polar decomposition for an arbitrary -unitary operator in a Hilbert space. This characterization has a quite different…
Truncated moment problems for -self-adjoint, -skew-self-adjoint and -unitary operators
Sergey M. Zagorodnyuk
In this paper we study truncated moment problems for -self-adjoint, -skew-self-adjoint and -unitary operators. Conditions of the solvability are given. Some canonical solu…
The truncated matrix trigonometric moment problem with an open gap
Sergey M. Zagorodnyuk
This paper is a continuation of our previous investigations on the truncated matrix trigonometric moment problem in Ukrainian Math. J., 2011, \textbf{63}, no. 6, 786-797, and Ukrai…
On the truncated matrix power moment problem with an open gap
Sergey M. Zagorodnyuk
In this paper we study the truncated power moment problem with an odd number of prescribed moments. A Nevanlinna-type formula is derived for this moment problem in the case when th…
Invertible extensions of symmetric operators and the corresponding generalized resolvents
Sergey M. Zagorodnyuk
In this paper we study invertible extensions of a symmetric operator in a Hilbert space . All such extensions are characterized by a parameter in the generalized Neumann's formu…
Generalized resolvents of symmetric and isometric operators: the Shtraus approach
Sergey M. Zagorodnyuk
This exposition paper is devoted to the theory of Abram Vilgelmovich Shtraus and his disciples and followers. This theory studies the so-called generalized resolvents of symmetric…
On the generalized resolvents of isometric operators with gaps
Sergey M. Zagorodnyuk
In this paper we obtain some slight correction and generalization of the results of Ryabtseva on the generalized resolvents for isometric operators with a gap in their spectrum. Al…
The Nevanlinna-type formula for the matrix Hamburger moment problem in a general case
Sergey M. Zagorodnyuk
In this paper we obtain a Nevanlinna-type formula for the matrix Hamburger moment problem in a general case. We only assume that the problem is solvable and has more that one solut…
The Nevanlinna-type formula for the truncated matrix trigonometric moment problem
Sergey M. Zagorodnyuk
This paper is a continuation of our previous investigation on the truncated matrix trigonometric moment problem in Ukrainian Math. J., 2011, 63, no.6, 786-797. In the present paper…
The Nevanlinna-Pick matrix interpolation in the Carathéodory class with infinite data both in the nondegenerate and degenerate cases
Sergey M. Zagorodnyuk
In this paper we study the Nevanlinna-Pick matrix interpolation problem in the Carathéodory class with infinite data (both in the nondegenerate and degenerate cases). We develop th…
The strong matrix Stieltjes moment problem
A. E. Choque Rivero, S. M. Zagorodnyuk
In this paper we study the strong matrix Stieltjes moment problem. We obtain necessary and sufficient conditions for its solvability. An analytic description of all solutions of th…
On the density of polynomials in some spaces
Sergey M. Zagorodnyuk
In this paper we study the density of polynomials in some spaces. Two choices of the measure and polynomials are considered: 1) a matrix non-negative Bor…
The truncated matrix trigonometric moment problem: the operator approach
Sergey M. Zagorodnyuk
In this paper we study the truncated matrix trigonometric moment problem. We obtained a bijective parameterization of all solutions of this moment problem (both in nondegenerate an…
On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum
Sergey M. Zagorodnyuk
In this paper we obtain necessary and sufficient conditions for a linear bounded operator in a Hilbert space to have a three-diagonal complex symmetric matrix with non-zero ele…
On the two-dimensional moment problem
Sergey M. Zagorodnyuk
In this paper we obtain an algorithm towards solving the two-dimensional moment problem. This algorithm gives the necessary and sufficient conditions for the solvability of the mom…