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Mat. Sb., 2005, Volume 196, Number 3, Pages 61–88 (Mi msb1276)  

This article is cited in 10 scientific papers (total in 10 papers)

Indeterminacy of interpolation problems in the Stieltjes class

Yu. M. Dyukarev

V. N. Karazin Kharkiv National University

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.

DOI: https://doi.org/10.4213/sm1276

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English version:
Sbornik: Mathematics, 2005, 196:3, 367–393

Bibliographic databases:

UDC: 517.5
MSC: Primary 47A57; Secondary 44A60, 30E05
Received: 03.06.2003

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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    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. Yu. M. Dyukarev, I. Yu. Serikova, “Complete indeterminacy of the Nevanlinna–Pick problem in the class $S[a,b]$”, Russian Math. (Iz. VUZ), 51:11 (2007), 17–29  mathnet  crossref  mathscinet  elib
    2. Yu. M. Dyukarev, “A Generalized Stieltjes Criterion for the Complete Indeterminacy of Interpolation Problems”, Math. Notes, 84:1 (2008), 22–37  mathnet  crossref  crossref  mathscinet  isi  elib
    3. Dyukarev Yu.M., Fritzsche B., Kirstein B., Mädler C., “On truncated matricial Stieltjes type moment problems”, Complex Anal. Oper. Theory, 4:4 (2010), 905–951  crossref  mathscinet  zmath  isi  elib
    4. Maxim Derevyagin, “The Jacobi matrices approach to Nevanlinna–Pick problems”, Journal of Approximation Theory, 163:2 (2011), 117  crossref  mathscinet  zmath  isi
    5. Yu. M. Dyukarev, A. E. Choque Rivero, “Criterion for the Complete Indeterminacy of the Nevanlinna–Pick Matrix Problem”, Math. Notes, 96:5 (2014), 651–665  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. 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
    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. Choque-Rivero A.E., “Relations Between the Orthogonal Matrix Polynomials on [a, B], Dyukarev-Stieltjes Parameters, and Schur Complements”, Spec. Matrices, 5:1 (2017), 303–318  crossref  mathscinet  zmath  isi
    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
    10. 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
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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