The strict Positivstellensatz for global analytic functions and the moment problem for semianalytic sets
type: Item
instance of: scholarly article
title: The strict Positivstellensatz for global analytic functions and the moment problem for semianalytic sets
zbMATH Open document ID: 0978.14003
published in: Mathematische Annalen
publication date: 2001-07-23T00:00:00Z
review text: 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.
reviewed by: Zbigniew Hajto
Mathematics Subject Classification ID: 14A05
Mathematics Subject Classification ID: 44A60
Mathematics Subject Classification ID: 14P15
zbMATH DE Number: 1463206
zbMATH Keywords: Positivstellensatz
zbMATH Keywords: global semianalytic set
zbMATH Keywords: \(K\)-moment problem
author: Francesca Acquistapace
author: Carlos Andradas
author: Fabrizio Broglia
MaRDI profile type: Publication
full work available at URL: s002080050346
OpenAlex ID: W1982000647
DOI: 10.1007/S002080050346
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description: scientific article; zbMATH DE number 1463206