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On Markov Moment Problem and Mazur-Orlicz Theorem

DOI: 10.4236/oalib.1103950, PP. 1-10

Subject Areas: Function Theory, Geometry, Algebraic Geometry

Keywords: Markov Moment Problem, Inequalities, Convex Subsets, Hahn-Banach Principle, Concrete Spaces

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Abstract

Applications of the generalization of Mazur-Orlicz theorem to concrete spaces are proved. Suitable moment problems are solved, as applications of extension theorems of linear operators with a convex and a concave constraint. In particular, a relationship between Mazur-Orlicz theorem and Markov moment problem is partially illustrated. In the end of this work, an application to the multidimensional Markov moment problem of an earlier extension result on a distanced subspace with respect to a bounded convex set is proved. Contrary to preceding results based on this theorem, now the solution is defined on a space of continuous functions vanishing at the origin. Most of the solutions are operator valued, respectively function valued.

Cite this paper

Olteanu, O. and Mihaila, J. M. (2017). On Markov Moment Problem and Mazur-Orlicz Theorem. Open Access Library Journal, 4, e3950. doi: http://dx.doi.org/10.4236/oalib.1103950.

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