Extremal Solutions of the Two-DimensionalL-Problem of Moments, II

AbstractThe extremal solutions of the truncatedL-problem of moments in two real variables, with support included in a given compact set, are described as characteristic functions of semi-algebraic sets given by a single polynomial inequality. An exponential kernel, arising as the determinantal function of a naturally associated hyponormal operator with rank-one self-commutator, on the other hand provides a defining function for these semi-algebraic sets and, on the other hand, encodes in a closed form their moments. In order to understand the finite determination structure of the extremal sequences of moments we study analytic continuation properties of the corresponding exponential kernel and, separately, some cyclicity properties of the associated hyponormal operator. An intrinsic characterization of the exponential kernel is also discussed