APPLICATION OF LOCALIZATION TO THE MULTIVARIATE MOMENT PROBLEM II

作者：Marshall Murray^*

来源：Mathematica Scandinavica, 2017, 120(1): 124-128.

DOI：10.7146/math.scand.a-25508

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), 171191) and is similar in nature to Schmiidgen's criterion in Marshall [5] and Schmudgen, 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 = Pi(n)(i=1) (1 + x(i)(2)) or p' = Pi(n-1)(i=1) (1 + x(i)(2)).

• 出版日期2017
• 单位Saskatoon; Saskatchewan