Octav Olteanu, Markov moment problem and approximation, 2014 (2014), Article ID 1 (January 25 2014)

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In this paper, we start by recalling some polynomial approximation results on unbounded subsets of R^n. Namely one approximates nonnegative continuous functions with compact support by sums of tensor products of positive polynomials on the positive semiaxes, in each separate variable. For such polynomials, expression in terms of sums of squares is well known. This method leads to characterization of the existence of the solution of the multidimensional Markov moment problem in terms of quadratic mappings. Two other applications related to the Markov moment problem are considered. Here the main ingredients of the proofs are extension of linear operator’s results, involving two constraints.


How to Cite this Article:

Octav Olteanu, Markov moment problem and approximation, Communications in Optimization Theory 2014 (2014), Article ID 1.