an:00008828
Zbl 0744.44008
Schm??dgen, Konrad
The \(K\)-moment problem for compact semi-algebraic sets
EN
Math. Ann. 289, No. 2, 203-206 (1991).
00156638
1991
j
44A60 14P10
\(K\)-moment problem; compact semi-algebraic sets
Suppose \(K\) is a closed subset of \(\mathbb{R}^ d\). A function \(f: \mathbb{N}^ d_ 0\to R\) is called a \(K\)-moment sequences if there exists a positive Borel measure \(\mu\in M(\mathbb{R}^ d)\) supported by \(K\) such that \(f(\alpha)\) is the \(\alpha\)-th moment of \(\mu\), i.e., \(f(\alpha)=\int x^ \alpha d\mu\), \(\forall\alpha\in\mathbb{N}^ d_ 0\). The main result of this note characterizes the \(K\)-moment sequences for compact semi- algebraic sets \(K\). Theorem 1 subsumes the above and proves a conjecture of Berg and Maserick [see \textit{C. Berg}, Moments in mathematics. AMS Short Course, San Antonia/Tex. 1987, Proc. Symp. Appl. Math. 37, 110-124 (1987; Zbl 0636.44007)].
R.N.Kalia (St.Cloud)
Zbl 0636.44007