Nodal systems with maximal domain of exactness for Gaussian quadrature formulas

The aim of this work is to study quadrature formulas for measures on the complex plane. The novelty of our contribution is to consider the exactness on subspaces of polynomials on the variables z   and z¯. Using this approach we characterize, in a unified way, the classical nodal systems for measures on the real line and the nodal systems for measures on the unit circle, which are based on para-orthogonal polynomials. We also characterize the nodal systems on the unit circle, which are not based on para-orthogonal polynomials (only for the case of nodal systems with 1 or 2 points).