Finite Gap Jacobi Matrices, I. The Isospectral Torus

Jacob Stordal Christiansen

doi:10.1007/s00365-009-9057-z

Finite Gap Jacobi Matrices, I. The Isospectral Torus

Jacob Stordal Christiansen

Department of Mathematical Sciences

19 Citations (Scopus)

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.

Original language	English
Journal	Constructive Approximation
Volume	32
Issue number	1
Pages (from-to)	1-65
Number of pages	65
ISSN	0176-4276
DOIs	https://doi.org/10.1007/s00365-009-9057-z
Publication status	Published - Aug 2010

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title = "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.",

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AU - Christiansen, Jacob Stordal

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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.

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DO - 10.1007/s00365-009-9057-z

M3 - Journal article

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SP - 1

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JO - Constructive Approximation

JF - Constructive Approximation

IS - 1

ER -

Finite Gap Jacobi Matrices, I. The Isospectral Torus

Abstract

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