2018
Том 70
№ 5

All Issues

Dudkin M. Ye.

Articles: 4
Article (Ukrainian)

Jacobi-type block matrices corresponding to the two-dimensional moment problem: polynomials of the second kind and Weyl function

Dudkin M. Ye., Kozak V. I.

↓ Abstract

Ukr. Mat. Zh. - 2016. - 68, № 4. - pp. 495-505

We continue our investigations of Jacobi-type symmetric matrices corresponding to the two-dimensional real power moment problem. We introduce polynomials of second kind and the corresponding analog of the Weyl function.

Brief Communications (Ukrainian)

Point spectrum of the schrödinger operator with point interactions at the vertices of regular N-gons

Dudkin M. Ye.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 8. - pp. 1128–1134

We present a complete description of the point spectrum of the Laplace operator perturbed by point potentials concentrated at the vertices of regular polygons. We prove a criterion for the absence of points of the point spectrum of a singular perturbed positive self-adjoint operator with the property of cyclicity of defect vectors.

Brief Communications (Ukrainian)

On the Point Spectrum of Self-Adjoint Operators That Appears under Singular Perturbations of Finite Rank

Dudkin M. Ye., Koshmanenko V. D.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 9. - pp. 1269-1276

We discuss purely singular finite-rank perturbations of a self-adjoint operator A in a Hilbert space ℋ. The perturbed operators \(\tilde A\) are defined by the Krein resolvent formula \((\tilde A - z)^{ - 1} = (A - z)^{ - 1} + B_z \) , Im z ≠ 0, where B z are finite-rank operators such that dom B z ∩ dom A = |0}. For an arbitrary system of orthonormal vectors \(\{ \psi _i \} _{i = 1}^{n < \infty } \) satisfying the condition span |ψ i } ∩ dom A = |0} and an arbitrary collection of real numbers \({\lambda}_i \in {\mathbb{R}}^1\) , we construct an operator \(\tilde A\) that solves the eigenvalue problem \(\tilde A\psi _i = {\lambda}_i {\psi}_i , i = 1, \ldots ,n\) . We prove the uniqueness of \(\tilde A\) under the condition that rank B z = n.

Brief Communications (Ukrainian)

Analog of the Krein Formula for Resolvents of Normal Extensions of a Prenormal Operator

Dudkin M. Ye.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2002. - 54, № 4. - pp. 555-562

We prove a formula that relates resolvents of normal operators that are extensions of a certain prenormal operator. This formula is an analog of the Krein formula for resolvents of self-adjoint extensions of a symmetric operator. We describe properties of the defect subspaces of a prenormal operator.