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Polynomial Approximation on Unbounded Subsets, Markov Moment Problem and Other Applications

Author

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  • Octav Olteanu

    (Department of Mathematics-Informatics, University Politehnica of Bucharest, 060042 Bucharest, Romania)

Abstract

This paper starts by recalling the author’s results on polynomial approximation over a Cartesian product A of closed unbounded intervals and its applications to solving Markov moment problems. Under natural assumptions, the existence and uniqueness of the solution are deduced. The characterization of the existence of the solution is formulated by two inequalities, one of which involves only quadratic forms. This is the first aim of this work. Characterizing the positivity of a bounded linear operator only by means of quadratic forms is the second aim. From the latter point of view, one solves completely the difficulty arising from the fact that there exist nonnegative polynomials on ℝ n , n ≥ 2 , which are not sums of squares.

Suggested Citation

  • Octav Olteanu, 2020. "Polynomial Approximation on Unbounded Subsets, Markov Moment Problem and Other Applications," Mathematics, MDPI, vol. 8(10), pages 1-12, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1654-:d:419538
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    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

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