Perturbations of orthogonal polynomials with periodic recursion coefficients

Pages 1931-2010 from Volume 171 (2010), Issue 3 by David Damanik, Rowan Killip, Barry Simon

Abstract

The results of Denisov-Rakhmanov, Szegő-Shohat-Nevai, and Killip-Simon are extended from asymptotically constant orthogonal polynomials on the real line (OPRL) and unit circle (OPUC) to asymptotically periodic OPRL and OPUC. The key tool is a characterization of the isospectral torus that is well adapted to the study of perturbations.

Mathematical Subject Classification

Primary 2000: Secondary:

DOI
https://doi.org/http://doi.org/10.4007/annals.2010.171.1931
MR
2680401
zbMATH
1194.47031
Milestones
Received: 2 February 2007
Revised: 3 September 2008
Accepted: 5 December 2008
Published online: 25 May 2010

Authors

David Damanik

Department of Mathematics
Rice University
Houston, TX 77005
United States

Rowan Killip

Department of Mathematics
University of California Los Angeles
Box 951555
Los Angeles, CA 90095-1555
United States

Barry Simon

Mathematics 253-37
California Institute of Technology
Pasadena, CA 91125
United States