Application of localization to the multivariate moment problem II - Marshall, Murray (MATHEMATICA SCANDINAVICA, 2017)
The paper is a sequel to the paper [5], Math. Scand. 115 (2014), 269–286, by the same author. A new criterion is presented for a PSD linear map L R[x] → R to correspond to a positive Borel measure on R^n. The criterion is stronger than Nussbaum’s criterion (Ark. Math. 6 (1965), 171–191) and is similar in nature to Schmüdgen’s criterion in Marshall [5] and Schmüdgen, Ark. Math. 29 (1991), 277–284. 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 R[x]. This latter result extends a result of Lasserre, Trans. Amer. Math. Soc. 365 (2013), 2489–2504. The techniques employed are the same localization techniques employed already in Marshall (Cand. Math. Bull. 46 (2003), 400–418, and [5]), specifically one works in the localization of R[x] at p = _i=1^n(1+x_i^2) or p’ = _i=1^n-1(1+x_i^2).