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Sbornik: Mathematics, 2005, Volume 196, Issue 3, Pages 367–393
DOI: https://doi.org/10.1070/SM2005v196n03ABEH000884 (Mi sm1276) 		 
This article is cited in 13 scientific papers (total in 13 papers)

Indeterminacy of interpolation problems in the Stieltjes class

Yu. M. Dyukarev

V. N. Karazin Kharkiv National University
English version PDF (302 kB) Citations (13)
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DOI: https://doi.org/10.1070/SM2005v196n03ABEH000884
Abstract: The concept of ordered families of interpolation problems in the Stieltjes class is introduced. Ordered families are used for the introduction of the concept of limiting interpolation problem in the same class. The limiting interpolation problem is proved to be soluble. A criterion for the complete indeterminacy of a limiting interpolation problem in the Stieltjes class is obtained. All solutions in the completely indeterminate case are described in terms of linear fractional transformations. General constructions are illustrated by the examples of the Stieltjes moment problem and the Nevanlinna–Pick problem in the Stieltjes class.
Received: 03.06.2003
Russian version:
Matematicheskii Sbornik, 2005, Volume 196, Number 3, Pages 61–88
DOI: https://doi.org/10.4213/sm1276
Bibliographic databases:
UDC: 517.5
MSC: Primary 47A57; Secondary 44A60, 30E05
Language: English
Original paper language: Russian
Citation: Yu. M. Dyukarev, “Indeterminacy of interpolation problems in the Stieltjes class”, Mat. Sb., 196:3 (2005), 61–88; Sb. Math., 196:3 (2005), 367–393
Citation in format AMSBIB
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    • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник - 1992–2005 Sbornik: Mathematics
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    English version PDF:15
    References:70
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