2015/02/03 by Konrad Schmüdgen, Schmüdgen, Konrad
Mathematics · #14P10 #44A60 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:14P10 #msc:44A60
paper · pdf · doi:10.48550/arxiv.1502.00825
The paper is based on the previous paper by the author arXiv:1406.0282 "A characterization of moment sequences by extensions"
arxiv created 2015/07/08 · arxiv updated 2015/07/09
The fibre theorem \citeschm2003 for the moment problem on closed semi-algebraic subsets of \Rd is generalized to finitely generated real unital algebras. As an application two new theorems on the rational multidimensional moment problem are proved. Another application is a characterization of moment functionals on the polynomial algebra \R[x1,…,xd] in terms of extensions. Finally, the fibre theorem and the extension theorem are used to reprove basic results on the complex moment problem due to Stochel and Szafraniec \citestochelsz and Bisgaard \citebisgaard.