Damanik, David and Killip, Rowan and Simon, Barry (2010) Perturbations of orthogonal polynomials with periodic recursion coefficients. Annals of Mathematics, 171 (3). pp. 1931-2010. ISSN 0003-486X http://resolver.caltech.edu/CaltechAUTHORS:20100803-145828608
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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.
|Additional Information:||© 2010 Annals of Mathematics. Received February 2, 2007. Revised September 3, 2008. Published 25 April 2010. It is a pleasure to thank Leonid Golinskii, Irina Nenciu, Leonid Pastur, and Peter Yuditskii for useful discussions. Note Added August, 2008. During the refereeing of this paper, Remling (in ), motivated in part by this paper, found a positive resolution of the conjecture that, in the language of our Theorem 9.5, every set in G is a Denisov-Rakhmanov set. His analysis depends on a very interesting theorem on right limits of Jacobi matrices with absolutely continuous spectrum—it provides a new approach to Denisov-Rakhmanov theorems. D.D. was supported in part by NSF grants DMS-0500910 and DMS-0653720. R.K. was supported in part by NSF grant DMS-0401277 and a Sloan Foundation Fellowship. B.S. was supported in part by NSF grant DMS-0140592 and U.S.-Israel Binational Science Foundation (BSF) Grant No. 2002068.|
|Classification Code:||Mathematical Subject Classification: Primary: 47B36; Secondary: 42C05|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||03 Aug 2010 22:31|
|Last Modified:||26 Dec 2012 12:17|
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