Perturbations of Orthogonal Polynomials With Periodic Recursion Coefficients

Details Perturbations of Orthogonal Polynomials With Periodic Recursion Coefficients Perturbations of Orthogonal Polynomials With Periodic Recursion Coefficients

2007-02-13

arxiv.org/abs/math/0702388v2

Mathematics

Spectral Theory

64 pages, to appear in Ann. of Math

Scientific paper

We extend the results of Denisov-Rakhmanov, Szego-Shohat-Nevai, and
Killip-Simon 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.

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