11 citations · 55 across the 38 of their papers we have counts for
17 papers · 1 filter
On the orthogonality of solutions for higher-order non-Hermitian difference equations
Sergey M. Zagorodnyuk
In this paper we study higher-order difference equations which can be written as follows: where is a -d…
An analytical parameterization for all solutions of the two-dimensional moment problem under Carleman-type conditions
Sergey M. Zagorodnyuk
The two-dimensional moment problem consists of finding a positive Borel measure in such that , , wher…
The truncated multidimensional moment problem: canonical solutions
Sergey M. Zagorodnyuk
For the truncated multidimensional moment problem we introduce a notion of a canonical solution. Namely, canonical solutions are those solutions which are generated by commuting se…
Positive orthogonalizing weights on the unit circle for the generalized Bessel polynomials
Sergey M. Zagorodnyuk
In this paper we study the generalized Bessel polynomials (in the notation of Krall and Frink). Let , . In this case we present th…
On some hypergeometric Sobolev orthogonal polynomials with several continuous parameters
Sergey M. Zagorodnyuk
In this paper we study the following hypergeometric polynomials: $\mathcal{P}_n(x) = \mathcal{P}_n(x;α,β,δ_1,\dots,δ_ρ,κ_1,\dots,κ_ρ) = {}_{ρ+2} F_{ρ+1} (-n,n+α+β+1,δ_1+1,\dots,δ_ρ…
On bounded complex Jacobi matrices and related moment problems
Sergey M. Zagorodnyuk
In this paper we study the linear functional on complex polynomials which is associated to a bounded complex Jacobi matrix . The associated moment problem is considered: fin…