Markov Moment Problem in Concrete Spaces Revisited

Authors

Keywords:

Classical and abstract Markov moment problem; concrete spaces; polynomial approximation on unbounded subsets, Markov Moment Problem, Concrete Spaces, Polynomial Approximation On Unbounded Subsets

Abstract

This review paper starts by recalling two main results on abstract Markov moment problem. Corresponding applications to problems involving concrete spaces of functions and self-adjoint operators are proved in detail. Some modified versions of such results are discussed. In the end, using polynomial approximation on special unbounded closed subsets, some multidimensional Markov moment problem on such subsets are recalled, without repeating the proofs. Our approximation results solve the difficulty arising from the fact that there exist positive polynomials on ,  which cannot be written as sums of squares of polynomials. However, the upper constraint of the solution is written in terms of products of quadratic forms. The solution are operators having as codomain an order complete Banach lattice. The latter space might be a commutative algebra of self-adjoint operators. All solutions obtained in this paper are continuous, and thanks to the density of polynomials in the involved domain function spaces, their uniqueness follows too. Operator valued solutions for classical moment problem are pointed out.

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Author Biography

Octav Olteanu, Politehnica University of Bucharest

Department of Mathematics-Informatics, full Professor.

References

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Published

2020-04-30

How to Cite

Octav Olteanu, & Janina Mihaela Mihaila. (2020). Markov Moment Problem in Concrete Spaces Revisited. MathLAB Journal, 5, 82-91. Retrieved from http://purkh.com/index.php/mathlab/article/view/663

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Section

Research Articles