  The power moments of a positive measure on the real line or the circle are
characterized by the non-negativity of an infinite matrix, Hankel, respectively
Toeplitz, attached to the data. Except some fortunate configurations, in higher
dimensions there are no non-negativity criteria for the power moments of a
measure to be supported by a prescribed closed set. We combine two well studied
fortunate situations, specifically a class of curves in two dimensions
classified by Scheiderer and Plaumann, and compact, basic semi-algebraic sets,
with the aim at enlarging the realm of geometric shapes on which the power
moment problem is accessible and solvable by non-negativity certificates.
