Lagrange interpolation with exponential weights on [formula omitted

Abstract

In order to approximate functions defined on (−1,1) with exponential growth for |x|→1, we consider interpolation processes based on the zeros of orthonormal polynomials with respect to exponential weights. Convergence results and error estimates in weighted Lp metric and uniform metric are given. In particular, in some function spaces, the related interpolating polynomials behave essentially like the polynomial of best approximation.