Geodesic
Indeterminacy Criteria for the Stieltjes Matrix Moment Problem
Matematičeskie zametki, Tome 75 (2004) no. 1, pp. 71-88.

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

In this paper, we obtain criteria for the indeterminacy of the Stieltjes matrix moment problem. We obtain explicit formulas for Stieltjes parameters and study the multiplicative structure of the resolvent matrix. In the indeterminate case, we study the analytic properties of the resolvent matrix of the moment problem. We describe the set of all matrix functions associated with the indeterminate Stieltjes moment problem in terms of linear fractional transformations over Stieltjes pairs. 
@article{MZM_2004_75_1_a6,
     author = {Yu. M. Dyukarev},
     title = {Indeterminacy {Criteria} for the {Stieltjes} {Matrix} {Moment} {Problem}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {71--88},
     publisher = {mathdoc},
     volume = {75},
     number = {1},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_75_1_a6/}
}
TY  - JOUR
AU  - Yu. M. Dyukarev
TI  - Indeterminacy Criteria for the Stieltjes Matrix Moment Problem
JO  - Matematičeskie zametki
PY  - 2004
SP  - 71
EP  - 88
VL  - 75
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2004_75_1_a6/
LA  - ru
ID  - MZM_2004_75_1_a6
ER  - 
%0 Journal Article
%A Yu. M. Dyukarev
%T Indeterminacy Criteria for the Stieltjes Matrix Moment Problem
%J Matematičeskie zametki
%D 2004
%P 71-88
%V 75
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2004_75_1_a6/
%G ru
%F MZM_2004_75_1_a6
Yu. M. Dyukarev. Indeterminacy Criteria for the Stieltjes Matrix Moment Problem. Matematičeskie zametki, Tome 75 (2004) no. 1, pp. 71-88. http://geodesic.mathdoc.fr/item/MZM_2004_75_1_a6/

[1] Stieltjes T., “Recherches sur les fractions continues”, Anns. Fac. Sci. Univ. Toulouse, 1894, no. 8, 1–122 ; 1895, no. 9, 1–47 | MR | Zbl

[2] Simon B., “The classical moment problem as a self-adjoint finite difference operator”, Adv. in Math., 137 (1998), 82–203 | DOI | MR | Zbl

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

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

[5] Dyukarev Yu. M., Choke Rivero A. E., “Stepennaya problema momentov na kompaktnom intervale”, Matem. zametki, 69:2 (2001), 200–213 | MR | Zbl

[6] Potapov V. P., “Drobno-lineinye preobrazovaniya matrits”, Issledovaniya po teorii operatorov i ikh prilozheniyam, ed. V. A. Marchenko, Naukova dumka, Kiev, 1979, 75–97 | MR

[7] Donoghue W. F., Monotone matrix functions and analytic continuation, Springer-Verlag, 1974 | MR | Zbl

[8] Orlov S. A., “Gnezdyaschiesya matrichnye krugi, analiticheski zavisyaschie ot parametra i teoremy ob invariantnosti rangov radiusov predelnykh matrichnykh krugov”, Izv. AN SSSR. Ser. matem., 40:3 (1976), 593–644 | MR | Zbl

[9] Potapov V. P., “K teorii matrichnykh krugov Veilya”, Funktsionalnyi analiz i prikladnaya matematika, ed. V. A. Marchenko, Naukova dumka, Kiev, 1982, 113–121 | MR

[10] Dyukarev Yu. M., “Faktorizatsiya operator-funktsii multiplikativnogo klassa Stiltesa”, Dokl. NAN Ukrainy, 2000, no. 9, 23–26 | MR | Zbl

[11] Dyukarev Yu. M., “Multiplikativnaya struktura rezolventnykh matrits interpolyatsionnykh zadach v klasse Stiltesa”, Vestn. Kharkovskogo un-ta. Ser. Matem., prikladnaya matem. i mekh., 1999, no. 458, 143–153 | Zbl

[12] Potapov V. P., “Teorema o module”, Teoriya funktsii, funktsion. analiz i ikh prilozh., 1983, no. 39, 95–106 | MR | Zbl

[13] Dyukarev Yu. M., Katsnelson V. E., “Multiplikativnye i additivnye klassy Stiltesa analiticheskikh matrits-funktsii i svyazannye s nimi interpolyatsionnye zadachi”, Teoriya funktsii, funktsion. analiz i ikh prilozh., 1981, no. 36, 13–27 | MR | Zbl

[14] Bolotnikov V., Sakhnovich L., “On an operator approach to interpolation problems for Stieltjes fanctions”, Integral Equations Operator Theory, 1999, no. 35, 423–470 | DOI | MR | Zbl