Real Algebraic and Analytic Geometry
Submission: 2014, September 27.
The paper is a sequel to an earlier paper by the same author. A new criterion is presented for a PSD linear functional L on the algebra of polynomials in n variables with real coefficients to correspond to a positive Borel measure on real n-space. The criterion is stronger than a criterion of A.E. Nussbaum (1965) and is similar in nature to a criterion of K. Schmudgen (1991). It is also explained how the criterion allows one to understand the support of the associated measure in terms of the non-negativity of L on a quadratic module of the polynomial algebra. This latter result extends a result of J.B. Lasserre (2013). The techniques employed are the same localization techniques employed already in the earlier paper. .
Mathematics Subject Classification (2000): 44A60, 14P99.
Keywords and Phrases: positive definite, moments, sums of squares, Carleman condition.
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