Geodesic
Perturbations of orthogonal polynomials with periodic recursion coefficients
David Damanik1 ; Rowan Killip2 ; Barry Simon3
1Department of Mathematics<br/>Rice University<br/>Houston, TX 77005<br/>United States
2Department of Mathematics<br/>University of California Los Angeles<br/>Box 951555<br/>Los Angeles, CA 90095-1555<br/>United States
3Mathematics 253-37<br/>California Institute of Technology<br/>Pasadena, CA 91125<br/>United States
Annals of mathematics, Tome 171 (2010) no. 3, pp. 1931-2010
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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.

DOI : 10.4007/annals.2010.171.1931

David Damanik  1   ; Rowan Killip  2   ; Barry Simon  3

1 Department of Mathematics<br/>Rice University<br/>Houston, TX 77005<br/>United States
2 Department of Mathematics<br/>University of California Los Angeles<br/>Box 951555<br/>Los Angeles, CA 90095-1555<br/>United States
3 Mathematics 253-37<br/>California Institute of Technology<br/>Pasadena, CA 91125<br/>United States 
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David Damanik; Rowan Killip; Barry Simon. Perturbations of orthogonal polynomials with periodic recursion coefficients. Annals of mathematics, Tome 171 (2010) no. 3, pp. 1931-2010. doi: 10.4007/annals.2010.171.1931

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