Damanik, David and Simon, Barry (2006) Jost functions and Jost solutions for Jacobi matrices, I. A necessary and sufficient condition for Szegő asymptotics. Inventiones Mathematicae, 165 (1). pp. 1-50. ISSN 0020-9910. doi:10.1007/s00222-005-0485-5. https://resolver.caltech.edu/CaltechAUTHORS:20170725-145819291
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Abstract
We provide necessary and sufficient conditions for a Jacobi matrix to produce orthogonal polynomials with Szegő asymptotics off the real axis. A key idea is to prove the equivalence of Szegő asymptotics and of Jost asymptotics for the Weyl solution. We also prove L^2 convergence of Szegő asymptotics on the spectrum.
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Additional Information: | © 2006 Springer-Verlag. Received: 22 February 2005; Accepted: 10 October 2005; First Online: 09 January 2006. Supported in part by NSF grant DMS-0227089. Supported in part by NSF grant DMS-0140592 and in part by Grant No. 2002068 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel. | |||||||||||||||
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Issue or Number: | 1 | |||||||||||||||
DOI: | 10.1007/s00222-005-0485-5 | |||||||||||||||
Record Number: | CaltechAUTHORS:20170725-145819291 | |||||||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170725-145819291 | |||||||||||||||
Official Citation: | Damanik, D. & Simon, B. Invent. math. (2006) 165: 1. https://doi.org/10.1007/s00222-005-0485-5 | |||||||||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||||||||
ID Code: | 79350 | |||||||||||||||
Collection: | CaltechAUTHORS | |||||||||||||||
Deposited By: | Tony Diaz | |||||||||||||||
Deposited On: | 25 Jul 2017 22:03 | |||||||||||||||
Last Modified: | 15 Nov 2021 17:47 |
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