Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

Finite Gap Jacobi Matrices, II. The Szego{double acute} Class

Christiansen, Jacob S. LU ; Simon, Barry and Zinchenko, Maxim (2011) In Constructive Approximation 33(3). p.365-403
Abstract

Let e ⊂ ℝ be a finite union of disjoint closed intervals. We study measures whose essential support is e and whose discrete eigenvalues obey a 1/2-power condition. We show that a Szego{double acute} condition is equivalent to (this includes prior results of Widom and Peherstorfer-Yuditskii). Using Remling's extension of the Denisov-Rakhmanov theorem and an analysis of Jost functions, we provide a new proof of Szego{double acute} asymptotics, including L2 asymptotics on the spectrum. We make heavy use of the covering map formalism of Sodin-Yuditskii as presented in our first paper in this series.

Please use this url to cite or link to this publication:
author
; and
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Isospectral torus, Orthogonal polynomials, Szego{double acute} asymptotics
in
Constructive Approximation
volume
33
issue
3
pages
39 pages
publisher
Springer
external identifiers
  • scopus:79953029428
ISSN
0176-4276
DOI
10.1007/s00365-010-9094-7
language
English
LU publication?
no
id
96ae5dad-b23b-4864-a1db-c5beb4e29285
date added to LUP
2025-07-11 12:14:39
date last changed
2025-10-14 11:52:43
@article{96ae5dad-b23b-4864-a1db-c5beb4e29285,
  abstract     = {{<p>Let e ⊂ ℝ be a finite union of disjoint closed intervals. We study measures whose essential support is e and whose discrete eigenvalues obey a 1/2-power condition. We show that a Szego{double acute} condition is equivalent to (this includes prior results of Widom and Peherstorfer-Yuditskii). Using Remling's extension of the Denisov-Rakhmanov theorem and an analysis of Jost functions, we provide a new proof of Szego{double acute} asymptotics, including L<sup>2</sup> asymptotics on the spectrum. We make heavy use of the covering map formalism of Sodin-Yuditskii as presented in our first paper in this series.</p>}},
  author       = {{Christiansen, Jacob S. and Simon, Barry and Zinchenko, Maxim}},
  issn         = {{0176-4276}},
  keywords     = {{Isospectral torus; Orthogonal polynomials; Szego{double acute} asymptotics}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{365--403}},
  publisher    = {{Springer}},
  series       = {{Constructive Approximation}},
  title        = {{Finite Gap Jacobi Matrices, II. The Szego{double acute} Class}},
  url          = {{http://dx.doi.org/10.1007/s00365-010-9094-7}},
  doi          = {{10.1007/s00365-010-9094-7}},
  volume       = {{33}},
  year         = {{2011}},
}