Christoffel functions for multiple orthogonal polynomials

Abstract

GRZEGORZ ŚWIDERSKI AND WALTER VAN ASSCHE A. We study weak asymptotic behaviour of the Christoffel-Darboux kernel on the main diagonal corresponding to multiple orthogonal polynomials. We show that under some hypotheses the weak limit of 1 ( , ) d is the same as the limit of the normalized zero counting measure of type II multiple orthogonal polynomials. We also study an extension of Nevai's operators to our context.