Selective approximate identities for orthogonal polynomial sequences

Let (Pn)n∈N0 be an orthogonal polynomial sequence on the real line with respect to a probability measure π with compact support S. For y ∈ S, a sequence of polynomials (B y n )n∈N0 is called a selective approximate identity with respect to y if limn→∞ B y n (x)f (x) dπ(x) = f (y) for all f ∈ C(S). We prove the existence and give a complete characterization of a selective approximate identity depending on (Pn)n∈N0 . A Fejér-like construction is performed and is considered in the context of Nevai class M(b,a) and Nevai’s G-operator.  2003 Elsevier Science (USA). All rights reserved.