On the Real Multidimensional Rational K-Moment Problem

2008/07/12 by Jaka Cimprič, Jaka Cimpric, Cimpric, Jaka +4
Computer Science · Mathematics · #14P99 #44A60 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical functions and polynomials #Polynomial and algebraic computation #math.AG #math.FA #msc:14P99 #msc:44A60

paper · pdf · doi:10.48550/arxiv.0807.1967

20 pages

openalex publication_date 2008/07/12 · arxiv created 2009/10/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 X=(X₁,...,X_n) such that the corresponding basic closed semialgebraic set K_S is nonempty. Let E=D^-1R[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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