Christoffel functions for multiple orthogonal polynomials

Abstract

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 1nKn(x,x)dμ 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.