Compact perturbations of orthogonal polynomials

Paul Nevai and Walter Van Assche

Vol. 153 (1992), No. 1, 163–184

DOI: 10.2140/pjm.1992.153.163

Abstract

We investigate orthogonal polynomials on the real line defined by a recurrence relation for which the recurrence coefficients behave asymptotically like a given system of recurrence coefficients. We give the asymptotic behavior of the orthogonal polynomials (relative to the given comparison system of orthogonal polynomials) and from this we deduce properties of the orthogonality measure.

Mathematical Subject Classification 2000

Primary: 42C05

Milestones

Received: 27 July 1990

Revised: 3 June 1991

Published: 1 March 1992