On the Real Multidimensional Rational K-Moment Problem

Details On the Real Multidimensional Rational K-Moment Problem On the Real Multidimensional Rational K-Moment Problem

2008-07-12

arxiv.org/abs/0807.1967v2

Mathematics

Algebraic Geometry

20 pages

Scientific paper

We present a solution to the real multidimensional rational K-moment problem, where K is defined by finitely many polynomial inequalities. More precisely, let S be a finite set of real polynomials in X=(X_1,...,X_n) such that the corresponding basic closed semialgebraic set K_S is nonempty. Let E=D^{-1}R[X] be a localization of the real polynomial algebra, and T_S^E the preordering on E generated by S. We show that every linear functional L on E that is nonnegative on T_S^E is represented by a positive measure on a certain subset of K_S, provided D contains an element that grows fast enough on K_S.

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