Geodesic
The criterion for the complete indeterminacy of limiting interpolation problem of Stieltjes type in terms of the orthonormal matrix functions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2015), pp. 3-16.

Voir la notice de l'article provenant de la source Math-Net.Ru

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
Mots-clés : orthonormal matrix functions. 
@article{IVM_2015_4_a0,
     author = {Yu. M. Dyukarev},
     title = {The criterion for the complete indeterminacy of limiting interpolation problem of {Stieltjes} type in terms of the orthonormal matrix functions},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--16},
     publisher = {mathdoc},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2015_4_a0/}
}
TY  - JOUR
AU  - Yu. M. Dyukarev
TI  - The criterion for the complete indeterminacy of limiting interpolation problem of Stieltjes type in terms of the orthonormal matrix functions
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2015
SP  - 3
EP  - 16
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2015_4_a0/
LA  - ru
ID  - IVM_2015_4_a0
ER  - 
%0 Journal Article
%A Yu. M. Dyukarev
%T The criterion for the complete indeterminacy of limiting interpolation problem of Stieltjes type in terms of the orthonormal matrix functions
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2015
%P 3-16
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2015_4_a0/
%G ru
%F IVM_2015_4_a0
Yu. M. Dyukarev. The criterion for the complete indeterminacy of limiting interpolation problem of Stieltjes type in terms of the orthonormal matrix functions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2015), pp. 3-16. http://geodesic.mathdoc.fr/item/IVM_2015_4_a0/

[1] Stieltjes T. J., “Recherches sur les fractions continues”, Ann. Fac. Sci., Toulouse Sci. Math. Sci. Phys., 8:4 (1894), 1–122 | MR

[2] Stieltjes T. J., “Recherches sur les fractions continues”, Ann. Fac. Sci., Toulouse Sci. Math. Sci. Phys., 9:1 (1895), 1–47 | MR

[3] Hamburger H., “Über eine Erweiterung des Stieltjesschen Momentenproblems”, Math. Ann., 81:2–4 (1920), 235–319 | DOI | MR | Zbl

[4] Hamburger H., “Über eine Erweiterung des Stieltjesschen Momentenproblems”, Math. Ann., 82:1–2 (1921), 120–164 | MR

[5] Hamburger H., “Über eine Erweiterung des Stieltjesschen Momentenproblems”, Math. Ann., 82:3–4 (1921), 168–187 | DOI | MR | Zbl

[6] Schur I., “Über Potenzreihen, die im Innern des Einheitskreises beschränkt sind”, J. Reine und Angew. Math., 147 (1917), 205–232

[7] Schur I., “Über Potenzreihen, die im Innern des Einheitskreises beschränkt sind”, J. Reine und Angew. Math., 148 (1918), 122–145 | Zbl

[8] Kovalishina I. V., Potapov V. P., “Indefinitnaya metrika v probleme Nevanlinny–Pika”, Dokl. AN ArmSSR, 59:1 (1974), 17–22 | MR | Zbl

[9] Kovalishina I. V., Potapov V. P., “Radiusy kruga Veilya v matrichnoi probleme Nevanlinny–Pika”, Teoriya operatorov v funktsionalnykh prostranstvakh i ee prilozheniya, Sb. nauch. tr., Nauk. dumka, Kiev, 1981, 25–49 | MR

[10] Potapov V. P., “K teorii matrichnykh krugov Veilya”, Funktsionalnyi analiz i prikladnaya matematika, Sb. nauchn. tr., Nauk. dumka, Kiev, 1982, 113–121 | MR

[11] Kovalishina I. V., “Analiticheskaya teoriya odnogo klassa interpolyatsionnykh zadach”, Izv. AN SSSR. Ser. matem., 47:3 (1983), 455–497 | MR | Zbl

[12] Dyukarev Yu. M., Katsnelson V. E., “Multiplikativnye i additivnye klassy Stiltesa analiticheskikh matrits-funktsii i svyazannye s nimi interpolyatsionnye zadachi”, Teoriya funktsii, funkts. analiz i ikh prilozh., 36, 1981, 13–27 | MR | Zbl

[13] Dyukarev Yu. M., “O kriteriyakh neopredelennosti matrichnoi problemy momentov Stiltesa”, Matem. zametki, 75:1 (2004), 71–88 | DOI | MR | Zbl

[14] Dyukarev Yu. M., “O neopredelennosti interpolyatsionnykh zadach v klasse Stiltesa”, Matem. sb., 196:3 (2005), 61–88 | DOI | MR | Zbl

[15] Dyukarev Yu. M., “Obobschennyi kriterii Stiltesa polnoi neopredelennosti interpolyatsionnykh zadach”, Matem. zametki, 84:1 (2008), 23–39 | DOI | MR

[16] Dyukarev Yu. M., “Obschaya skhema resheniya interpolyatsionnykh zadach v klasse Stiltesa, osnovannaya na soglasovannykh integralnykh predstavleniyakh par neotritsatelnykh operatorov. I”, Matem. fiz., analiz, geometriya, 6:1/2 (1999), 30–54 | MR | Zbl

[17] Bolotnikov V., Sakhnovich L., “On an operator approach to interpolation problems for Stieltjes functions”, Integral Equat. Oper. Theory, 35 (1999), 423–470 | DOI | MR | Zbl

[18] Krein M. G., Nudelman A. A., Problema momentov Markova i ekstremalnye zadachi, Nauka, M., 1973 | MR