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Matematicheskie Zametki, 2008, Volume 84, Issue 1, Pages 23–39
DOI: https://doi.org/10.4213/mzm5192 (Mi mzm5192) 		 
This article is cited in 14 scientific papers (total in 14 papers)

A Generalized Stieltjes Criterion for the Complete Indeterminacy of Interpolation Problems

Yu. M. Dyukarev

V. N. Karazin Kharkiv National University
Full-text PDF (571 kB) Citations (14)
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DOI: https://doi.org/10.4213/mzm5192
Abstract: The main result of this paper is a generalized Stieltjes criterion for the complete indeterminacy of interpolation problems in the Stieltjes class. This criterion is a generalization to limit interpolation problems of the classical Stieltjes criterion for the indeterminacy of moment problems. It is stated in terms of the Stieltjes parameters $M_j$ and $N_j$. We obtain explicit formulas for the Stieltjes parameters. General constructions are illustrated by examples of the Stieltjes moment problem and the Nevanlinna–Pick problem in the Stieltjes class.
Keywords: interpolation problem, Stieltjes moment problem, Stieltjes criterion for indeterminacy, Nevanlinna–Pick problem, Stieltjes operator function, Hankel matrix.
Received: 10.04.2006
Revised: 05.02.2007
English version:
Mathematical Notes, 2008, Volume 84, Issue 1, Pages 22–37
DOI: https://doi.org/10.1134/S000143460807002X
Bibliographic databases:
UDC: 517.5
Language: Russian
Citation: Yu. M. Dyukarev, “A Generalized Stieltjes Criterion for the Complete Indeterminacy of Interpolation Problems”, Mat. Zametki, 84:1 (2008), 23–39; Math. Notes, 84:1 (2008), 22–37
Citation in format AMSBIB
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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