Real Algebraic and Analytic Geometry
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256. Jaka Cimprič, Murray Marshall, Tim Netzer:
On the real multidimensional rational $K$-moment problem.

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Submission: 2008, July 12.

Abstract:
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 $\underline{X}=(X_1,\ldots,X_n)$ such that the corresponding basic closed semialgebraic set $K_S$ is nonempty. Let $E=D^{-1}\RR[\underline{X}]$ 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 $E$ such that $L(T_S^E) \ge 0$ is represented by a positive measure $\mu$ on a certain subset of $K_S$, provided $D$ contains an element that grows fast enough on $K_S$.

Mathematics Subject Classification (2000): 44A60, 14P99.

Keywords and Phrases: moment problem, positive polynomials, sums of squares.

Full text, 20p.: dvi 89k, ps.gz 202k, pdf 264k.