The strict Positivstellensatz for global analytic functions and the moment problem for semianalytic sets
This paper gives an interesting improvement of Stengle's Positivstellensatz for strict inequalities. The authors show that analytic functions strictly positive on a global semianalytic set \(X=\{f_1\geq 0,\dots,f_k\geq 0\}\) have a representation \(s_0^2+s_1^2f_1+\cdots +s_k^2f_k\) with \(s_j^2>0\) over \(\mathbb R^n\). As a corollary they give also a new proof of the week analytic Positivstellensatz and extend \textit{K. Schmüdgen}'s results [Math. Ann. 289, 203-206 (1991; Zbl 0744.44008)] to the analytic frame.
scientific article; zbMATH DE number 1463206