Complex moment matrices via Halmos-Bram and Embry conditions

Abstract

By considering a bridge between Bram-Halmos and Embry characterizations for the subnormality of cyclic operators, we extend the Curto-Fialkow and Embry truncated complex moment problem, and solve the problem finding the finitely atomic representing measure mu such that gamma ij = integral z(-i)z(j)d mu, (0 <= i+j <= 2n, vertical bar i-j vertical bar <= n+s, 0 <= s <= n); the cases of s = n and s = 0 are induced by Bram-Halmos and Embry characterizations, respectively. The former is the Curto-Fialkow truncated complex moment problem and the latter is the Embry truncated complex moment problem.