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Recursiveness, positivity, and truncated moment problems. (English) Zbl 0757.44006
Suppose, there are \(m\) complex numbers \(\gamma_ 0,\gamma_ 1,\dots,\gamma_ m\). Let \(K\) be a subset of \(\mathbb{C}\). The truncated \(K\)- power moment problem is the question of finding a positive Borel measure \(\mu\) such that \(\int t^ j d\mu(t)=\gamma_ j\) (\(0\leq j\leq m\)) and \(\text{supp} \mu\subseteq K\). The authors consider the cases \(K=\mathbb{R}\), \([a,b]\), \([0,+\infty)\) and \(T=\{t\in \mathbb{C}\): \(| t | =1\}\). They give a detailed description of necessary and sufficient conditions for solvability of the moment problem. They obtain a lot of classical results and state many new ones.
Reviewer: E.Krätzel (Jena)

MSC:
44A60 Moment problems
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