Strong asymptotics on the support of the measure of orthogonality for polynomials orthogonal with respect to a discrete Sobolev inner product

Abstract

In (6, 8) relative asymptotics for Sobolev orthogonal polynomials were studied. When the continuous part of the measure satisfies the Szegýo condition, the strong asymptotics outside the support of the measure follow from (6, 8). In this paper, we analyze this problem on the support of the measure. 1. Introduction and statements of results Some problems arising from approximation theory, mathematical physics, and number theory have motivated different generalizations of the standard notion of orthogonality. If µ is a finite positive Borel measure supported on the real line, then {pn} is the sequence of standard orthonormal polynomials (OP) with respect to µ when