Mehrdimensionales Momentenproblem und Schur-Algorithmus
Zusammenfassung der Projektergebnisse
The aim of the project was to study the multidimensional moment problem in terms of the multidimensional Stieltjes transform as the interpolation problem and construct the Schur algorithm for the truncated multidimensional moment problem. The obtained results were related to classical and indefinite multidimensional moment problems and can also be applied to the multidimensional moment problem for atomic measure. Several stepby-step algorithms were obtained, which were based on different approaches. The first and basic was two-dimensional moment problem, one was studied separately from the multidimensional case. The truncated multidimensional moment problem was reformulated in terms of the multidimensional Stieltjes transform as the interpolation problem and also was studied. The relation between one-dimensional and multidimensional moment problems was obtained. Hence, the obtained Schur algorithms for the multidimensional moment problem were base on the one-dimensional case. The description of all solution was found in terms P, J and S–fractions. The Padé approximants of the the truncated multidimensional moment problem were found. In additional, the description of all solutions of the full multidimensional moment problem and the indeterminate criterion for the full multidimensional moment problem were obtained. Moreover, the Herglotz-Nevanlinna class functions in several variables was also studied. The asymptotic expansion of the Herglotz-Nevanlinna class functions in several variables was obtained. The corresponding interpolation problem in this class was formulated and solved. All project goals were achieved.
Projektbezogene Publikationen (Auswahl)
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Two-Dimensional Moment Problem and Schur Algorithm. Integral Equations and Operator Theory, 97(1).
Kovalyov, Ivan & Kunis, Stefan
