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From Hahn–Banach Type Theorems to the Markov Moment Problem, Sandwich Theorems and Further Applications

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  • Octav Olteanu

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

Abstract

The aim of this review paper is to recall known solutions for two Markov moment problems, which can be formulated as Hahn–Banach extension theorems, in order to emphasize their relationship with the following problems: (1) pointing out a previously published sandwich theorem of the type f ≤ h ≤ g , where f , − g are convex functionals and h is an affine functional, over a finite-simplicial set X , and proving a topological version for this result; (2) characterizing isotonicity of convex operators over arbitrary convex cones; giving a sharp direct proof for one of the generalizations of Hahn–Banach theorem applied to the isotonicity; (3) extending inequalities assumed to be valid on a small subset, to the entire positive cone of the domain space, via Krein–Milman or Carathéodory’s theorem. Thus, we point out some earlier, as well as new applications of the Hahn–Banach type theorems, emphasizing the topological versions of these applications.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1328-:d:396884
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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. Octav Olteanu, 2013. "Moment Problems on Bounded and Unbounded Domains," International Journal of Analysis, Hindawi, vol. 2013, pages 1-7, January.
    4. Kleiber, Christian & Stoyanov, Jordan, 2013. "Multivariate distributions and the moment problem," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 7-18.
    5. Octav Olteanu, 2013. "New Results on Markov Moment Problem," International Journal of Analysis, Hindawi, vol. 2013, pages 1-17, February.
    Full references (including those not matched with items on IDEAS)

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