Complex moment problem and recursive relations - Idrissi, K.; Zerouali, E. H. (Methods of Functional Analysis and Topology, 2019)
We introduce a new methodology to solve the truncated complex moment problem. To this aim we investigate recursive doubly indexed sequences and their characteristic polynomials. A characterization of recursive doubly indexed moment sequences is given. A simple application gives a computable solution to the complex moment problem for cubic harmonic characteristic polynomials of the form z^3+az+bz, where a and b are arbitrary real numbers. We also recapture a recent result due to Curto-Yoo given for cubic column relations in M(3) of the form Z^3=itZ+uZ with t,u real numbers satisfying some suitable inequalities. Furthermore, we solve the truncated complex moment problem with column dependence relations of the form Z^k+1= _0≤ n+ m ≤ k a_nm Z^n Z^m (a_nm C).