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On Markov Moment Problem and Mazur-Orlicz Theorem

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

Subject Areas: Geometry, Function Theory, 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.

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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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