On Markov Moment Problem and Related Results

Symmetry

Octav Olteanu¹ 

[1] Department of Mathematics-Informatics, University Politehnica of Bucharest, Splaiul Independenţei 313, 060042 Bucharest, Romania;

关键词: polynomial approximation;    constrained extension of linear operators;    Markov moment problem;    self-adjoint operator;    symmetric matrix;    compact subset;   

DOI  :  10.3390/sym13060986

来源: DOAJ

【 摘 要 】

We prove new results and complete our recently published theorems on the vector-valued Markov moment problem, by means of polynomial approximation on unbounded subsets, also applying an extension of the positive linear operators’ result. The domain is the Banach lattice of continuous real-valued functions on a compact subset or an $L_{\nu }^1$ space, where $\nu$ is a positive moment determinate measure on a closed unbounded set. The existence and uniqueness of the operator solution are proved. Our solutions satisfy the interpolation moment conditions and are between two given linear operators on the positive cone of the domain space. The norm controlling of the solution is emphasized. The most part of the results are stated and proved in terms of quadratic forms. This type of result represents the first aim of the paper. Secondly, we construct a polynomial solution for a truncated multidimensional moment problem.

【 授权许可】

Unknown