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On the Moment Problem and Related Problems

Author

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  • Octav Olteanu

    (Department Mathematics-Informatics, University Politehnica of Bucharest, Splaiul Independenţei 313, 060042 Bucharest, Romania)

Abstract

Firstly, we recall the classical moment problem and some basic results related to it. By its formulation, this is an inverse problem: being given a sequence ( y j ) j ∈ ℕ n of real numbers and a closed subset F ⊆ ℝ n , n ∈ { 1 , 2 , … } , find a positive regular Borel measure μ on F such that ∫ F t j d μ = y j , j ∈ ℕ n . This is the full moment problem. The existence, uniqueness, and construction of the unknown solution μ are the focus of attention. The numbers y j , j ∈ ℕ n are called the moments of the measure μ . When a sandwich condition on the solution is required, we have a Markov moment problem. Secondly, we study the existence and uniqueness of the solutions to some full Markov moment problems. If the moments y j are self-adjoint operators, we have an operator-valued moment problem. Related results are the subject of attention. The truncated moment problem is also discussed, constituting the third aim of this work.

Suggested Citation

  • Octav Olteanu, 2021. "On the Moment Problem and Related Problems," Mathematics, MDPI, vol. 9(18), pages 1-26, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2289-:d:637373
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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. "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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