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Finite Gap Jacobi Matrices, I. The Isospectral Torus

Christiansen, Jacob S. and Simon, Barry and Zinchenko, Maxim (2010) Finite Gap Jacobi Matrices, I. The Isospectral Torus. Constructive Approximation, 32 (1). pp. 1-65. ISSN 0176-4276.

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Let e ⊂ R be a finite union of disjoint closed intervals. In the study of orthogonal polynomials on the real line with measures whose essential support is e, a fundamental role is played by the isospectral torus. In this paper, we use a covering map formalism to define and study this isospectral torus. Our goal is to make a coherent presentation of properties and bounds for this special class as a tool for ourselves and others to study perturbations. One important result is the expression of Jost functions for the torus in terms of theta functions.

Item Type:Article
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Simon, Barry0000-0003-2561-8539
Additional Information:© 2009 Springer. Received: 25 September 2008. Accepted: 11 February 2009. Published online: 22 May 2009. Communicated by Vilmos Totik. We want to thank D. Calegari, H. Farkas, F. Gesztesy, I. Kra, N. Makarov, F. Peherstorfer, and P. Yuditskii for helpful discussions and comments.
Funding AgencyGrant Number
Subject Keywords:Isospectral torus; Covering map; Orthogonal polynomials
Issue or Number:1
Classification Code:Mathematics Subject Classification (2000): 42C05 - 58J53 - 14H30
Record Number:CaltechAUTHORS:20100713-080234381
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19011
Deposited By: Tony Diaz
Deposited On:15 Jul 2010 22:06
Last Modified:03 Oct 2019 01:50

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