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

Mathematics

Octav Olteanu¹ 

[1] Department of Mathematics-Informatics, University Politehnica of Bucharest, 060042 Bucharest, Romania;

关键词: polynomial approximation;    Hahn–Banach theorem;    Markov moment problem;    determinacy;    quadratic forms;   

DOI  :  10.3390/math8101654

来源: DOAJ

【 摘 要 】

This paper starts by recalling the author’s results on polynomial approximation over a Cartesian product 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 operator only by means of quadratic forms is the second aim. From the latter point of view, one solves completely the difficulty arising from the fact that there exist nonnegative polynomials on, which are not sums of squares.

【 授权许可】

Unknown