Extension inside the disk of asymptotics for Sobolev orthogonal polynomials
In this paper, we consider a general Sobolev inner product on the unit circle of the following type: [GRAPHICS] with mu(j) (j = 0,..., p) finite positive Borel measures on [0, 2pi] and p a positive integer p greater than or equal to 1. Under the assumption that the Caratheodory functions of measures mu(0),..., mu(p-1) and the Szego function of measure mu(p) have analytic extension outside the open unit disk, we prove that Szego's asymptotic formula holds true for the Sobalev orthogonal polynomials. (C) 2003 Elsevier Ltd. All rights reserved.
orthogonal polynomials sobolev inner products szego's theory