Published June 2011
| Submitted
Journal Article
Open
Finite Gap Jacobi Matrices, II. The Szegő Class
Abstract
Let e ⊂ R be a finite union of disjoint closed intervals. We study measures whose essential support is e and whose discrete eigenvalues obey a 1/2-power condition. We show that a Szegő condition is equivalent to lim sup a_1...a_n/cap e_n >0 (this includes prior results of Widom and Peherstorfer-Yuditskii). Using Remling's extension of the Denisov-Rakhmanov theorem and an analysis of Jost functions, we provide a new proof of Szego asymptotics, including L^2 asymptotics on the spectrum. We make heavy use of the covering map formalism of Sodin-Yuditskii as presented in our first paper in this series.
Additional Information
© 2010 Springer Science+Business Media, LLC. Received: 31 May 2009. Revised: 9 October 2009. Accepted: 10 November 2009. Published online: 13 April 2010. Communicated by Vilmos Totik. J.S. Christiansen was supported in part by a Steno Research Grant from FNU, the Danish Research Council. B. Simon was supported in part by NSF grant DMS-0652919. Maxim Zinchenko was supported in part by NSF grant DMS-0965411. We would like to thank F. Peherstorfer and P. Yuditskii for the private communication [14]. J.S.C. would like to thank M. Flach and A. Lange for the hospitality of Caltech where this work was completed.Attached Files
Submitted - 0906.1630
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Additional details
- Eprint ID
- 23323
- DOI
- 10.1007/s00365-010-9094-7
- Resolver ID
- CaltechAUTHORS:20110414-085411774
- DMS-0652919
- NSF
- DMS-0965411
- NSF
- Danish Natural Science Research Council
- Created
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2011-04-14Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field