Geodesic
Power Moment Problem on Compact Intervals
Matematičeskie zametki, Tome 69 (2001) no. 2, pp. 200-213.

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

In this paper the power moment problem on the compact interval is studied. In the nondegenerate case the set of all solutions is described in terms of linear fractional transformations. An explicit formula for the resolvent matrix is given. 
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Yu. M. Dyukarev; A. E. Choque Rivero. Power Moment Problem on Compact Intervals. Matematičeskie zametki, Tome 69 (2001) no. 2, pp. 200-213. http://geodesic.mathdoc.fr/item/MZM_2001_69_2_a4/

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

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

[3] Ivanchenko T. S., Sakhnovich L. A., “Operatornyi podkhod k skheme V. P. Potapova issledovaniya interpolyatsionnykh zadach”, Ukr. matem. zh., 39:5 (1987), 573–578 | MR | Zbl

[4] Sakhnovich L. A., “Metod operatornykh tozhdestv”, Algebra i analiz, 5:1 (1993), 3–80 | MR | Zbl

[5] 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., 36 (1981), 13–27 | MR | Zbl

[6] Dyukarev Yu. M., “Integral representations of a pair of nonnegative operators and interpolation problems in the Stieltjes class”, Operator Theory: Advances and Applications, 95, 1997, 165–184 | MR | Zbl

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

[8] Atkinson F., Diskretnye i nepreryvnye granichnye zadachi, Mir, M., 1968 | Zbl

[9] Brodskii M. S., Treugolnye i zhordanovy predstavleniya lineinykh operatorov, Nauka, M., 1969