Application of Mhaskar-Prestin operators to the convergence of orthonormal expansions

Abstract

Let I be either R or (−1, 1),andletW : I → (0, ∞). Assume that W 2 is a weight. We study the quasi-interpolatory polynomial operators τ l,n,m introduced by Mhaskar and Prestin, for Freud weights, Erd˝os weights, and the e xponential weights on (−1, 1). We investigate boundedness of τ l,n,m in weighted L p spaces