Finite Gap Jacobi Matrices, I. The Isospectral Torus

TY - JOUR

T1 - Finite Gap Jacobi Matrices, I. The Isospectral Torus

AU - Christiansen, Jacob Stordal

PY - 2010/8

Y1 - 2010/8

N2 - 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.

AB - 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.

U2 - 10.1007/s00365-009-9057-z

DO - 10.1007/s00365-009-9057-z

M3 - Journal article

SN - 0176-4276

VL - 32

SP - 1

EP - 65

JO - Constructive Approximation

JF - Constructive Approximation

IS - 1

ER -