The moment problem for non-compact semialgebraic sets

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Optimization of Polynomial Functions (2003, background): “Following standard terminology [6][9][ 12 ][14][15] we say that the moment problem holds for MS if for each L 2 KS there exists a positive Borel measure µ on KS such that 8f 2 R[x], L(f) = R KS f dµ.”
Connes' embedding conjecture and sums of hermitian squares (2006, background): “Together with the fact that is homogeneous, [ PS , Lemma 2.7] shows that is a proper and therefore a closed map.”
Positivity, sums of squares and the multi-dimensional moment problem (2002, background): “At the end of [11], the authors announce that they can answer open problems 4, 6 and 7 above, based on unpublished work of Scheiderer [14].”
Sums of Squares, Moment Matrices and Optimization Over Polynomials (2009, background): “[111, 132] If K has a nonempty interior then Mt(g1, .”
Positivity, sums of squares and the multi-dimensional moment problem II ⁄ (2005, background): “When the present paper was submitted, Powers and Scheiderer informed us that they were also working on similar questions. Their paper has since appeared [ 11 ].”