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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