Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published August 2010 | Submitted
Journal Article Open

Finite Gap Jacobi Matrices, I. The Isospectral Torus

Abstract

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.

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.

Attached Files

Submitted - 0810.3273

Files

Files (711.4 kB)
Name Size Download all
md5:0d539611164e1eb641cac83139eca440
711.4 kB Download

Additional details

Created:
August 22, 2023
Modified:
October 20, 2023