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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, Number 4, Pages 3–16 (Mi ivm8985)  
This article is cited in 2 scientific papers (total in 2 papers)

The criterion for the complete indeterminacy of limiting interpolation problem of Stieltjes type in terms of the orthonormal matrix functions

Yu. M. Dyukarev

Chair of Mathematics and Physics, Belgorod State Agricultural Academy, 1 Vavilov str., Maiskii community, 308503 Russia
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Abstract: The main goal of this paper is to study the ordered sequences of generalized interpolation problems and the limiting interpolation problem in the Stieltjes class by using the orthonormal matrix functions. We obtain explicit formulas for the orthonormal matrix functions. The main result of the paper is a criterion for the complete indeterminacy of limiting interpolation problem in the Stieltjes class. General constructions are illustrated by examples of the Stieltjes moment problem and the Nevanlinna–Pick problem in the Stieltjes class.
Keywords: interpolation problems, Stieltjes functions, a criterion of complete indeterminacy, orthonormal matrix functions.
Received: 09.11.2013
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2015, Volume 59, Issue 4, Pages 1–12
DOI: https://doi.org/10.3103/S1066369X15040015
Bibliographic databases:
Document Type: Article
UDC: 517.518
Language: Russian
Citation: Yu. M. Dyukarev, “The criterion for the complete indeterminacy of limiting interpolation problem of Stieltjes type in terms of the orthonormal matrix functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 4, 3–16; Russian Math. (Iz. VUZ), 59:4 (2015), 1–12
Citation in format AMSBIB
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\by Yu.~M.~Dyukarev
\paper The criterion for the complete indeterminacy of limiting interpolation problem of Stieltjes type in terms of the orthonormal matrix functions
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2015
\issue 4
\pages 3--16
\mathnet{http://mi.mathnet.ru/ivm8985}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2015
\vol 59
\issue 4
\pages 1--12
\crossref{https://doi.org/10.3103/S1066369X15040015}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84925834584}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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