Extension of Linear Operators and Polynomial Approximation, with Applications to Markov Moment Problem and Mazur-Orlicz Theorem

Keywords: Extension of Linear Operators, Markov Moment Problem, Mazur-Orlicz Theorem, Polynomial Approximation on Unbounded Subsets, Concrete Spaces

Abstract

One recalls the relationship between the Markov moment problem and extension of linear functionals (or operators), with two constraints. One states necessary and sufficient conditions for the existence of solutions of some abstract vector-valued Markov moment problems, by means of a general Hahn-Banach principle. The classical moment problem is discussed as a particular important case. A short section is devoted to applications of polynomial approximation in studying the existence and uniqueness of the solutions for two types of Markov moment problems. Mazur-Orlicz theorem is also recalled and applied. We use general type results in studying related problems which involve concrete spaces of functions and self-adjoint operators. Sometimes, the uniqueness of the solution follows too. Most of our solutions are operator-valued or function-valued.

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Published
2019-04-30
How to Cite
Olteanu, O. (2019). Extension of Linear Operators and Polynomial Approximation, with Applications to Markov Moment Problem and Mazur-Orlicz Theorem. MathLAB Journal, 2(1), 91-109. Retrieved from http://purkh.com/index.php/mathlab/article/view/307
Section
Research Articles