Szegő's theorem on Parreau−Widom sets
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/3448166
- author
- Christiansen, Jacob Stordal LU
- publishing date
- 2012
- 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
- 2016-04-01 11:14:50
- date last changed
- 2022-03-12 21:00:30
@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}}, keywords = {{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}}, doi = {{10.1016/j.aim.2011.09.012}}, volume = {{229}}, year = {{2012}}, }