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New Results on Markov Moment Problem

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  • Octav Olteanu

Abstract

The present work deals with the existence of the solutions of some Markov moment problems. Necessary conditions, as well as necessary and sufficient conditions, are discussed. One recalls the background containing applications of extension results of linear operators with two constraints to the moment problem and approximation by polynomials on unbounded closed finite-dimensional subsets. Two domain spaces are considered: spaces of absolute integrable functions and spaces of analytic functions. Operator valued moment problems are solved in the latter case. In this paper, there is a section that contains new results, making the connection to some other topics: bang-bang principle, truncated moment problem, weak compactness, and convergence. Finally, a general independent statement with respect to polynomials is discussed.

Suggested Citation

  • Octav Olteanu, 2013. "New Results on Markov Moment Problem," International Journal of Analysis, Hindawi, vol. 2013, pages 1-17, February.
    • Handle: RePEc:hin:ijanal:901318
    DOI: 10.1155/2013/901318
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    References listed on IDEAS

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    1. Laurent Gosse & Olof Runborg, 2008. "Existence, uniqueness and a constructive solution algorithm for a class of finite Markov moment problems," Post-Print hal-00323346, HAL.
    2. Laurent Gosse & Olof Runborg, 2008. "Existence, uniqueness and a constructive solution algorithm for a class of finite Markov moment problems," Papers 0809.3714, arXiv.org.
    3. Kleiber, Christian & Stoyanov, Jordan, 2013. "Multivariate distributions and the moment problem," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 7-18.
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    Cited by:

    1. Octav Olteanu, 2021. "On the Moment Problem and Related Problems," Mathematics, MDPI, vol. 9(18), pages 1-26, September.
    2. Octav Olteanu, 2020. "From Hahn–Banach Type Theorems to the Markov Moment Problem, Sandwich Theorems and Further Applications," Mathematics, MDPI, vol. 8(8), pages 1-16, August.

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