Moment Problems on Bounded and Unbounded Domains

الملخص EN

Using approximation results, we characterize the existence of the solution for a two-dimensional moment problem in the first quadrant, in terms of quadratic forms, similar to the one-dimensional case.

For the bounded domain case, one considers a space of complex analytic functions in a disk and a space of continuous functions on a compact interval.

The latter result seems to give sufficient (and necessary) conditions for the existence of a multiplicative solution.