Overview of anti-Gaussian quadrature formulas on the space of multiple orthogonal polynomials with nearly diagonal multi-indeces

Abstract

Multiple orthogonal polynomials represent a generalization of orthogonal polynomials in the sense that they satisfy the orthogonality conditions with respect to r∈N different weight functions simultaneously. In this presentation, we will provide an overview of the set of anti-Gaussian quadrature formulas for the optimal set of quadrature formulas in Borges’ sense on the spaces of algebraic and trigonometric polynomials, while limiting ourselves to nearly diagonal multi-indices. The corresponding multiple orthogonal polynomials that arise in the construction of these quadrature formulas satisfy the orthogonality conditions with respect to r bilinear forms that naturally emerge from the mentioned constructions.