Ukrainian Mathematical Journal

, Volume 55, Issue 7, pp 1061–1070 | Cite as

Existence Theorems for Generalized Moment Representations

  • A. P. Golub


We establish conditions for the existence of generalized moment representations introduced by Dzyadyk in 1981.


Existence Theorem Moment Representation Generalize Moment Representation 
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  1. 1.
    V. K. Dzyadyk, “On a generalization of the moment problem,” Dokl. Akad. Nauk Ukr. SSR, No. 6, 8–12 (1981).Google Scholar
  2. 2.
    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).Google Scholar
  3. 3.
    A. P. Golub, Generalized Moment Representations and Rational Approximations [in Russian], Preprint No. 25, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1987).Google Scholar
  4. 4.
    N. I. Akhiezer, Classical Moment Problem and Some Related Problems of Analysis [in Russian], Fizmatgiz, Moscow (1961).Google Scholar
  5. 5.
    V. K. Dzyadyk, Approximation Methods for the Solution of Differential and Integral Equations [in Russian], Naukova Dumka, Kiev (1988).Google Scholar
  6. 6.
    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).Google Scholar
  7. 7.
    F. R. Gantmakher, Theory of Matrices [in Russian], Nauka, Moscow (1967).Google Scholar
  8. 8.
    G. A. Baker, Jr., and P. Graves-Morris, Padé Approximants, Addison-Wesley, London (1981).Google Scholar
  9. 9.
    D. Z. Arov, “Passive linear stationary dynamical systems,” Sib. Mat. Zh., 20, No. 2, 211–228 (1979).Google Scholar
  10. 10.
    A. P. Golub, “On joint Padé approximations of a collection of degenerate hypergeometric functions,” Ukr. Mat. Zh., 39, No. 6, 701–706 (1987).Google Scholar
  11. 11.
    A. I. Markushevich, Theory of Analytic Functions [in Russian], Vol. 2, Nauka, Moscow (1968).Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • A. P. Golub
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev

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