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Izv. Vyssh. Uchebn. Zaved. Mat., 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

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.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2015, 59:4, 1–12

UDC: 517.518
Received: 09.11.2013

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
\Bibitem{Dyu15}
\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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. M. Dyukarev, I. Yu. Serikova, “Step-by-step solving of ordered interpolational problem for Stieltjes functions”, Russian Math. (Iz. VUZ), 61:6 (2017), 13–26  mathnet  crossref  isi
    2. Abdon E. Choke-Rivero, “Rezolventnaya matritsa usechennoi matrichnoi interpolyatsionnoi problemy Nevanlinny–Pika i ortogonalnye ratsionalnye funktsii klassa Stiltesa”, Izv. vuzov. Matem., 2019, no. 6, 65–79  mathnet  crossref
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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