Solving moment problems by dimensional extension

Abstract

The first part of this paper is devoted to an analysis of moment problems in R^n with supports contained in a closed set defined by finitely many polynomial inequalities. The second part of the paper uses the representation results of positive functionals on certain spaces of rational functions developed in the first part, for decomposing a polynomial which is positive on such a semi-algebraic set into a canonical sum of squares of rational functions times explicit multipliers.

arXiv comment21 pages, published version, abstract added in migration

Cited by in corpus (5)

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• The Truncated Moment Problem for Unital Commutative R-Algebras
• Positive polynomials on unbounded domains
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• Sparse non-SOS Putinar-type Positivstellensätze