Abstract
We establish conditions for the existence of generalized moment representations introduced by Dzyadyk in 1981.
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REFERENCES
V. K. Dzyadyk, “On a generalization of the moment problem,” Dokl. Akad. Nauk Ukr. SSR, No. 6, 8–12 (1981).
V. K. Dzyadyk and A. P. Golub, Generalized Moment Problem and Padé Approximation [in Russian], Preprint No. 58, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev(1981).
A. P. Golub, Generalized Moment Representations and Rational Approximations [in Russian], Preprint No. 25, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1987).
N. I. Akhiezer, Classical Moment Problem and Some Related Problems of Analysis [in Russian], Fizmatgiz, Moscow (1961).
V. K. Dzyadyk, Approximation Methods for the Solution of Differential and Integral Equations [in Russian], Naukova Dumka, Kiev (1988).
M. Abramowitz and I. A. Stegun (editors), Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, National Bureau of Standards, Appl. Math., Ser. 55 (1964).
F. R. Gantmakher, Theory of Matrices [in Russian], Nauka, Moscow (1967).
G. A. Baker, Jr., and P. Graves-Morris, Padé Approximants, Addison-Wesley, London (1981).
D. Z. Arov, “Passive linear stationary dynamical systems,” Sib. Mat. Zh., 20, No. 2, 211–228 (1979).
A. P. Golub, “On joint Padé approximations of a collection of degenerate hypergeometric functions,” Ukr. Mat. Zh., 39, No. 6, 701–706 (1987).
A. I. Markushevich, Theory of Analytic Functions [in Russian], Vol. 2, Nauka, Moscow (1968).
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Golub, A.P. Existence Theorems for Generalized Moment Representations. Ukrainian Mathematical Journal 55, 1061–1070 (2003). https://doi.org/10.1023/B:UKMA.0000010605.91548.77
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DOI: https://doi.org/10.1023/B:UKMA.0000010605.91548.77