Perturbations of orthogonal polynomials with periodic recursion coefficients


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.


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