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Jost functions and Jost solutions for Jacobi matrices, I. A necessary and sufficient condition for Szegő asymptotics

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. 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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s00222-005-0485-5DOIArticle
https://link.springer.com/article/10.1007%2Fs00222-005-0485-5PublisherArticle
https://arxiv.org/abs/math/0502486arXivDiscussion Paper
http://rdcu.be/utJFPublisherFree ReadCube access
ORCID:
AuthorORCID
Damanik, David0000-0001-5924-3849
Simon, Barry0000-0003-2561-8539
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.
Funders:
Funding AgencyGrant Number
NSFDMS-0227089
NSFDMS-0140592
Binational Science Foundation (USA-Israel)2002068
Issue or Number:1
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:09 Mar 2020 13:18

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