Abstract
Polynomial approximation results on unbounded subsets of \(R^n\) are discussed. By applying these results, one obtains characterizations of the existence of the solutions of the multidimensional vector valued moment problems in terms of quadratic mappings. Two other applications related to the Markov moment problem are considered. The main ingredients of the proofs are the extension of linear operator’s results, with two constraints. All sections contain statements using Hahn–Banach principle or its generalizations, as well as natural order relations on function or operator spaces. One solves the difficulty created by the existence of positive polynomials that are not sums of squares in several dimensions.
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Olteanu, O. Approximation and Markov moment problem on concrete spaces. Rend. Circ. Mat. Palermo 63, 161–172 (2014). https://doi.org/10.1007/s12215-014-0149-7
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DOI: https://doi.org/10.1007/s12215-014-0149-7