arXiv subjects
Publications and source records attributed to Ivan Kovalyov.
The multidimensional moment problem is studied in terms of the Steiltjes transform. The diagonal step-by-step algorithm is constructed for the multidimensional moment problem. The set of solutions of the full multidimensional moment problem is found in terms of the continued fractions. Moreover, the diagonal step-by-step algorithm can be applied to the special truncated multidimensional moment problem.
The truncated multidimensional moment problem is studied in terms of the Stieltjes transform as the interpolation problem. A step-by-step algorithm is constructed for the multidimensional moment problem and the set of solutions is found in terms of continued fractions.
We study a truncated two-dimensional moment problem in terms of the Stieltjes transform. The set of the solutions is described by the Schur step-by-step algorithm, which is based on the continued fraction expansion of the solution. In particular, the obtained results are applicable to the two-dimensional moment problem for atomic measures.
We study a localization of functions defined on Vilenkin groups. To measure the localization we introduce two uncertainty products $UP_λ$ and $UP_{G}$ that are similar to the Heisenberg uncertainty product. $UP_λ$ and $UP_{G}$ differ from each other by the metric used for the Vilenkin group $G$. We discuss analogs of a quantitative uncertainty principle. Representations for $UP_λ$ and $UP_{G}$ in terms of Walsh and Haar basis are given.
Nondegenerate truncated indefinite Stieltjes moment problem in the class $\mathbf{N}_κ^{k}$ of generalized Stieltjes functions is considered. To describe the set of solutions of this problem we apply the Schur step-by-step algorythm, which leads to the expansion of these solutions in generalized Stieltjes continuous fractions studied recently in \cite{DK15}. Explicit formula for the resolvent matrix in terms of generalized Stieltjes polynomials is found.