Asymptotics for Christoffel functions with varying weights (Q1841174)

The main result in this paper is the uniform asymptotic behaviour of the Christoffel function \(\lambda_n(w^{2n},x)\) of a varying weight \(w^{2n}\) which is defined on a closed set \(\Sigma\) consisting of a finite number of intervals. This result includes the asymptotics of the Christoffel function for Freud weights, as obtained earlier by \textit{D. S. Lubinsky} [``Strong asymptotics for extremal errors and polynomials associated with Erdős-type weights'' (1989; Zbl 0743.41001)]. Furthermore, it gives the asymptotic distribution of eigenvalues of random matrices (in a strong sense).