Finite and infinite gap Jacobi matrices
(2013) Fifth International Conference on Operator Theory Analysis and Mathematical Physics (OTAMP 2010) 227. p.43-55- Abstract
- The present paper reviews the theory of bounded Jacobi matrices whose essential spectrum is a finite gap set, and it explains how the theory can be extended to also cover a large number of infinite gap sets. Two of the central results are generalizations of Denisov–Rakhmanov’s theorem and Szegő’s theorem, including asymptotics of the associated orthogonal polynomials. When the essential spectrum is an interval, the natural limiting object J0 has constant Jacobi parameters. As soon as gaps occur, ℓ say, the complexity increases and the role of J0 is taken over by an ℓ -dimensional isospectral torus of periodic or almost periodic Jacobi matrices.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/3448252
- author
- Christiansen, Jacob Stordal LU
- publishing date
- 2013
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- Orthogonal polynomials, Szegő’s theorem, Isospectral torus, Parreau–Widom sets
- host publication
- Operator Theory Advances and Applications (Operator Methods in Mathematical Physics, Conference on Operator Theory, Analysis and Mathematical Physics (OTAMP) 2010, Bedlewo, Poland)
- editor
- Janas, Jan ; Kurasov, Pavel ; Laptev, Ari and Naboko, Sergey
- volume
- 227
- pages
- 13 pages
- publisher
- Birkhäuser
- conference name
- Fifth International Conference on Operator Theory Analysis and Mathematical Physics (OTAMP 2010)
- conference location
- Bedlewo, Poland
- conference dates
- 2010-08-05 - 2010-08-12
- external identifiers
-
- scopus:84922287774
- ISSN
- 2296-4878
- 0255-0156
- ISBN
- 978-3-0348-0531-5
- 978-3-0348-0530-8 (print)
- DOI
- 10.1007/978-3-0348-0531-5_2
- language
- English
- LU publication?
- no
- id
- 0780b4bc-1eb8-49e1-8e38-fafa8c4c0ac1 (old id 3448252)
- date added to LUP
- 2016-04-01 09:47:37
- date last changed
- 2024-08-11 05:46:27
@inproceedings{0780b4bc-1eb8-49e1-8e38-fafa8c4c0ac1, abstract = {{The present paper reviews the theory of bounded Jacobi matrices whose essential spectrum is a finite gap set, and it explains how the theory can be extended to also cover a large number of infinite gap sets. Two of the central results are generalizations of Denisov–Rakhmanov’s theorem and Szegő’s theorem, including asymptotics of the associated orthogonal polynomials. When the essential spectrum is an interval, the natural limiting object J0 has constant Jacobi parameters. As soon as gaps occur, ℓ say, the complexity increases and the role of J0 is taken over by an ℓ -dimensional isospectral torus of periodic or almost periodic Jacobi matrices.}}, author = {{Christiansen, Jacob Stordal}}, booktitle = {{Operator Theory Advances and Applications (Operator Methods in Mathematical Physics, Conference on Operator Theory, Analysis and Mathematical Physics (OTAMP) 2010, Bedlewo, Poland)}}, editor = {{Janas, Jan and Kurasov, Pavel and Laptev, Ari and Naboko, Sergey}}, isbn = {{978-3-0348-0531-5}}, issn = {{2296-4878}}, keywords = {{Orthogonal polynomials; Szegő’s theorem; Isospectral torus; Parreau–Widom sets}}, language = {{eng}}, pages = {{43--55}}, publisher = {{Birkhäuser}}, title = {{Finite and infinite gap Jacobi matrices}}, url = {{http://dx.doi.org/10.1007/978-3-0348-0531-5_2}}, doi = {{10.1007/978-3-0348-0531-5_2}}, volume = {{227}}, year = {{2013}}, }