Recursiveness, positivity, and truncated moment problems. (English) Zbl 0757.44006

Curto, Raúl E.; Fialkow, Lawrence A

Houston J. Math. 17, No. 4, 603-635 (1991).

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

Keywords:

truncated \(K\)-power moment problem; positive Borel measure