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Szegő's theorem on Parreau−Widom sets

Christiansen, Jacob Stordal LU (2012) In Advances in Mathematics 229(2). p.1180-1204
Abstract
In this paper, we generalize Szegőʼs theorem for orthogonal polynomials on the real line to infinite gap sets of Parreau–Widom type. This notion includes Cantor sets of positive measure. The Szegő condition involves the equilibrium measure which in turn is absolutely continuous. Our approach builds on a canonical factorization of the M-function and the covering space formalism of Sodin–Yuditskii.
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author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Szegő integral, Eigenvalue sums, Parreau–Widom sets
in
Advances in Mathematics
volume
229
issue
2
pages
1180 - 1204
publisher
Elsevier
external identifiers
  • scopus:82355175172
ISSN
0001-8708
DOI
10.1016/j.aim.2011.09.012
language
English
LU publication?
no
id
6b8db681-213d-4525-8486-c0afc83a402e (old id 3448166)
alternative location
http://www.sciencedirect.com/science/article/pii/S0001870811003562
date added to LUP
2013-09-06 18:41:36
date last changed
2017-11-12 03:17:13
@article{6b8db681-213d-4525-8486-c0afc83a402e,
  abstract     = {In this paper, we generalize Szegőʼs theorem for orthogonal polynomials on the real line to infinite gap sets of Parreau–Widom type. This notion includes Cantor sets of positive measure. The Szegő condition involves the equilibrium measure which in turn is absolutely continuous. Our approach builds on a canonical factorization of the M-function and the covering space formalism of Sodin–Yuditskii.},
  author       = {Christiansen, Jacob Stordal},
  issn         = {0001-8708},
  keyword      = {Szegő integral,Eigenvalue sums,Parreau–Widom sets},
  language     = {eng},
  number       = {2},
  pages        = {1180--1204},
  publisher    = {Elsevier},
  series       = {Advances in Mathematics},
  title        = {Szegő's theorem on Parreau−Widom sets},
  url          = {http://dx.doi.org/10.1016/j.aim.2011.09.012},
  volume       = {229},
  year         = {2012},
}