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Mat. Zametki, 2008, Volume 84, Issue 1, Pages 23–39 (Mi mz5192)  

This article is cited in 9 scientific papers (total in 9 papers)

A Generalized Stieltjes Criterion for the Complete Indeterminacy of Interpolation Problems

Yu. M. Dyukarev

V. N. Karazin Kharkiv National University

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

DOI: https://doi.org/10.4213/mzm5192

Full text: PDF file (571 kB)
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English version:
Mathematical Notes, 2008, 84:1, 22–37

Bibliographic databases:

UDC: 517.5
Received: 10.04.2006
Revised: 05.02.2007

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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Derevyagin M., “The Jacobi matrices approach to Nevanlinna-Pick problems”, J. Approx. Theory, 163:2 (2011), 117–142  crossref  mathscinet  zmath  isi  elib  scopus
    2. Dyukarev Yu.M., “Ortonormirovannye matritsy-funktsii i interpolyatsionnye zadachi v klasse Nevanlinny”, Nauchnye vedomosti Belgorodskogo gosudarstvennogo universiteta. Seriya: Matematika. Fizika, 32:19(162) (2013), 37–48  elib
    3. Yu. M. Dyukarev, “The criterion for the complete indeterminacy of limiting interpolation problem of Stieltjes type in terms of the orthonormal matrix functions”, Russian Math. (Iz. VUZ), 59:4 (2015), 1–12  mathnet  crossref
    4. Choque-Rivero A.E., “From the Potapov To the Krein-Nudel'Man Representation of the Resolvent Matrix of the Truncated Hausdorff Matrix Moment Problem”, Bol. Soc. Mat. Mex., 21:2 (2015), 233–259  crossref  mathscinet  zmath  isi
    5. Eddy A. River Ch., “on Dyukarev'S Resolvent Matrix For a Truncated Stieltjes Matrix Moment Problem Under the View of Orthogonal Matrix Polynomials”, Linear Alg. Appl., 474 (2015), 44–109  crossref  mathscinet  zmath  isi  scopus
    6. Yu. M. Dyukarev, “Geometric and operator measures of degeneracy for the set of solutions to the Stieltjes matrix moment problem”, Sb. Math., 207:4 (2016), 519–536  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    7. 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
    8. Fritzsche B. Kirstein B. Maedler C., “On a simultaneous approach to the even and odd truncated matricial Stieltjes moment problem II: An -Schur–Stieltjes-type algorithm for sequences of holomorphic matrix-valued functions”, Linear Alg. Appl., 520 (2017), 335–398  crossref  mathscinet  zmath  isi  scopus
    9. Yu. M. Dyukarev, “The zeros of determinants of matrix-valued polynomials that are orthonormal on a semi-infinite or finite interval”, Sb. Math., 209:12 (2018), 1745–1755  mathnet  crossref  crossref  adsnasa  isi  elib
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