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. 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.

Item Type:

Article

Related URLs:

URL	URL Type	Description
https://doi.org/10.1007/s00222-005-0485-5	DOI	Article
https://link.springer.com/article/10.1007%2Fs00222-005-0485-5	Publisher	Article
https://arxiv.org/abs/math/0502486	arXiv	Discussion Paper
http://rdcu.be/utJF	Publisher	Free ReadCube access

ORCID:

Author	ORCID
Damanik, David	0000-0001-5924-3849
Simon, Barry	0000-0003-2561-8539

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 Agency	Grant Number
NSF	DMS-0227089
NSF	DMS-0140592
Binational Science Foundation (USA-Israel)	2002068

Issue or Number:

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

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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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