The Nevanlinna theorem of the classical theory of moments revisited

• Autorzy: Urrea, M. , Tkachenko, I. M. , Fernández de Córdoba, P.
• Języki publikacji: EN

Abstrakty

EN

The canonical solutions of the truncated Hamburger moment problem (both in the classical and degenerate cases) are found. The Nevanlinna theorem which provides the noncanonical solutions of the truncated Hamburger problem is also rederived in the framework of the operator approach.

Słowa kluczowe

PL

momenty mocy; twierdzenie Nevanlinna; podejście operatora

EN

power moments; Nevanlinna`s theorem; operator approach

• Czasopismo: Journal of Applied Analysis
• Rocznik: 2001
• Tom: Vol. 7, nr 2
• Strony: 209-224
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Urrea, M.

• Department of Applied Mathematics ETSII, Polytechnic University E-46071 Valencia Spain,

autor

Tkachenko, I. M.

• Department of Applied Mathematics ETSII, Polytechnic University E-46071 Valencia Spain

autor

Fernández de Córdoba, P.

• Department of Applied Mathematics ETSII, Polytechnic University E-46071 Valencia Spain

Bibliografia

• [1] Adamyan, V. M. and Tkachenko, I. M., High-frequency electrical conductivity of a collisional plasma, High Temp. (USA) 21, (1983), 307.
• [2] Akhiezer, N. 1., The Classical Moment Problem and Some Related Questions in Analysis, Hafher Publishing Company, New York, 1965.
• [3] Akhiezer, N. I. and Glazman, I. M., Theory of Linear Operators in Hilbert Space, Frederick Ungar Publishing Company, New York, 1963, Vol II, § 59.
• [4] Curto, R. E. and Fialkow, L. A., Recursiveness, positivity, and truncated moment problems, Houston J. Math. 17 (1991), 603; see also: Curto, R. E. and Fialkow, L. A., Solutions of the Truncated Moment Problem, Mem. Amer. Math. Soc. 119 (1996).
• [5] Hamburger, H., Uber eine Erweiterung des Stieltjesschen Momentenproblems, Math. Ann. 81 (1920), 235; ibid, 82 (1921), 120; ibid, 82 (1921), 168.
• [6] Jones, W. B., Njâstad, O., Thron, W. J., Moment theory, orthogonal polynomials, quadrature, and continued fractions associated with the unit circle, Bull. London Math. Soc. 21 (1989), 113-152.
• [7] Krein, M. G., The theory of extensions of semibounded Hermitian operators and its applications (in Russian), Mat. Sb. 20 (1947), 431-495.
• [8] M.G. Krein, The description of all solutions of the truncated power moment problem and some problems of operator theory, Mat. Issled. 2(2) (1967), 114-132; English translation, Amer. Math. Soc. Transi. Ser. 2 95 (1970), 219-234.
• [9] Krein, M. G., Nudel’man, A. A., The Markov Moment Problem and Extremal Problems, Transi. Math. Monographs 50 (1977), Amer. Math. Soc., Providence, RI.
• [10] Landau, H. J. (Ed.), Moments in Mathematics, Proc. Sympos. Appl. Math. 37 (1987), Amer. Math. Soc., Providence, RI.
• [11] Ortner, J., Rylyuk, V. M., Tkachenko, I. M., Reflectivity of cold magnetized plasmas, Phys. Rev. E 50 (1994), 4937.
• [12] Shohat, J. A., Tamarkin, J. D., The Problem of Moments, Math. Surveys Monographs 1 (1943), Amer. Math. Soc., Providence, RI, (4th Ed. 1970).
• [13] Stieltjes, T. J., Recherches sur les fractions continues, Ann. Fac. Sei. Toulouse Math. 8 (1894), J76-J122; ibid, 9 (1895), A5-A47.