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
![[img]](http://authors.library.caltech.edu/style/images/fileicons/application_pdf.png) |
PDF
- Published Version
Restricted to Repository administrators only See Usage Policy. 1085Kb |
Use this Persistent URL to link to this item: http://resolver.caltech.edu/CaltechAUTHORS:20100803-145828608
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.
| Item Type: | Article | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 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 [94]), 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. | ||||||||||||||
| Funders: |
| ||||||||||||||
| Classification Code: | Mathematical Subject Classification: Primary: 47B36; Secondary: 42C05 | ||||||||||||||
| Record Number: | CaltechAUTHORS:20100803-145828608 | ||||||||||||||
| Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:20100803-145828608 | ||||||||||||||
| Related URLs: | |||||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||||
| ID Code: | 19264 | ||||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||||
| Deposited By: | Tony Diaz | ||||||||||||||
| Deposited On: | 03 Aug 2010 22:31 | ||||||||||||||
| Last Modified: | 26 Dec 2012 12:17 |
Repository Staff Only: item control page
