# Polynomial Approximation on Unbounded Subsets, Markov Moment Problem and Other Applications

```@inproceedings{Olteanu2020PolynomialAO,
title={Polynomial Approximation on Unbounded Subsets, Markov Moment Problem and Other Applications},
author={Octav Olteanu},
year={2020}
}```
This paper starts by recalling the author’s results on polynomial approximation over a Cartesian product A of closed unbounded intervals and its applications to solving Markov moment problems. Under natural assumptions, the existence and uniqueness of the solution are deduced. The characterization of the existence of the solution is formulated by two inequalities, one of which involves only quadratic forms. This is the first aim of this work. Characterizing the positivity of a bounded linear…
5 Citations
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New results and theorems on the vector-valued Markov moment problem are proved by means of polynomial approximation on unbounded subsets, also applying an extension of the positive linear operators’ result.
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A general extension theorem for linear operators with two constraints is recalled and applied to concrete spaces and found that Hahn–Banach type theorems for the extension of linear operators having a codomain such a space can be applied.
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