TITLE:
On Markov Moment Problem and Mazur-Orlicz Theorem
AUTHORS:
Octav Olteanu, Janina Mihaela Mihăilă
KEYWORDS:
Markov Moment Problem, Inequalities, Convex Subsets, Hahn-Banach Principle, Concrete Spaces
JOURNAL NAME:
Open Access Library Journal,
Vol.4 No.10,
October
25,
2017
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.