@inproceedings{0780b4bc1eb849e18e38fafa8c4c0ac1,
title = "Finite and infinite gap Jacobi matrices",
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{\textquoteright}s theorem and Szeg{\H o}{\textquoteright}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.",
keywords = "Orthogonal polynomials, Szeg{\H o}{\textquoteright}s theorem, Isospectral torus, Parreau–Widom sets",
author = "Christiansen, {Jacob Stordal}",
year = "2013",
doi = "10.1007/978-3-0348-0531-5_2",
language = "English",
isbn = "978-3-0348-0531-5",
volume = "227",
publisher = "Birkh{\"a}user Verlag",
pages = "43--55",
editor = "Jan Janas and Pavel Kurasov and Ari Laptev and Sergey Naboko",
booktitle = "Operator Theory Advances and Applications (Operator Methods in Mathematical Physics, Conference on Operator Theory, Analysis and Mathematical Physics (OTAMP) 2010, Bedlewo, Poland)",
address = "Switzerland",
note = "Fifth International Conference on Operator Theory Analysis and Mathematical Physics (OTAMP 2010) ; Conference date: 05-08-2010 Through 12-08-2010",
}