On multidimensional determinate moment sequences (Q2708135)

Multidimensional moment sequences are determinated by the author in order to solve a multidimensional moment problem in some infinite dimensional Banach spaces. The classical moment problem in the one dimensional case for eventually constant moment sequences is generalized to the so-called eventually \(d\)-periodic sequences. A detailed proof of the main theorems for each case is included. The author defines the notions of \(\underline{m}\)-complete sequences of Borel functions and \(\underline{c}\)-complete sequences and restricts to study \(\underline{m}\)-completeness for some specified classes of measures in connection with Boas's theorem, which asserts that given any sequence of real numbers \(m_n\) there exists a signed measure \(\mu\), such that \(\int^\infty_0 x^n d\mu(x)=m_n\).