Constructive approach to the truncated moment problem on reducible cubic curves: Hyperbolic type relations

Abstract

In this paper, we solve constructively the bivariate truncated moment problem (TMP) of even degree on reducible cubic curves, where the conic part is a hyperbola. According to the classification from our previous work, these represent three out of nine possible canonical forms of reducible cubic curves after applying an affine linear transformation. The TMP on the union of three parallel lines, the circular and the parabolic type TMP were solved constructively in our previous work, while in this paper we consider three cases of hyperbolic type, i.e., a type without real self-intersection points, a type with a simple real self-intersection point and a type with a double real self-intersection point. In all cases, we also establish bounds on the number of atoms in a minimal representing measure.