Solution of the Stieltjes truncated moment problem

• Autorzy: Adamyan V. M. , Tkachenko I. M. , Urrea M.
• Języki publikacji: EN

Abstrakty

EN

The conditions of solvability and description of all solutions of the truncated Stieltjes moment problem are obtained using as the starting point earlier results on the Hamburger truncated moment problem. An algebraic algorithm for the explicit solution of both problems is proposed.

Słowa kluczowe

EN

Stieltjes power moments; canonical solutions; Nevanlinna`s theorem

PL

chwile mocy Stieltjes'a; kanoniczne rozwiązania; twierdzenie Nevanlinna

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2003
• Tom: Vol. 9, nr 1
• Strony: 57--74
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Adamyan V. M.

• Department of Theoretical Physics Odessa National University Odessa, Ukraine

autor

Tkachenko I. M.

autor

Urrea M.

• Department of Applied Mathematics, Polytechnic University of Valencia, Valencia, Spain

Bibliografia

• [1] Adamyan, V. M., Tkachenko, I. M., Solution of the truncated matrix Hamburger moment problem according to M. G. Krein, in “Operator Theory and Related Topics”, Vol. II (Odessa, 1997), 33-51; Oper. Theory Adv. Appl. 118, Birkhauser, Basel, 2000.
• [2] Adamyan, V. M., Tkachenko, I. M., Truncated Hamburger moment problems with constraints, Recent progress in functional analysis (Proceedings of the International Functional Analysis Meeting on the Occasion of the 70th Birthday of Manuel Valdivia), Valencia, 2000, 321-333; North-Holland Math. Stud. 189 (2001), North-Holland, Amsterdam.
• [3] Curto, R. E., Fialkow, L. A., Recursiveness, positivity, and truncated moment problems, Houston J. Math. 17 (1991), 603-635.
• [4] Derkach, V. A., Malamud, M. M., Generalized resolvent of bounded Hermitian operators and the truncated moment problem (in Russian), Doki. Akad. Nauk Ukrainy 11 (1991), 34-39, 173
• [5] Krein, M. G., The theory of self-adjoint extensions of semi-bounded Hermitian transformations and its applications (in Russian), I, Rec. Math. [Mat. Sbornik] N. S. 20(62) (1947), 431-495; II, Mat. Sbornik N. S. 21(63) (1947), 365-404.
• [6] Krein M. G., Nudel’man A. A., The Markov moment problem and extremal problems (in Russian), Nauka, Moscow, 1973; Translations of Mathematical Monographs American Mathematical Society 50 (1977), Providence, RI.
• [7] Urrea, M., Tkachenko, I. M., Fernandez de Córdoba, P., The Nevanlinna theorem of the classical theory of moments revisited, J. Appl. Anal. 7 (2000), 209-224.