Finite and infinite gap Jacobi matrices

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Sammanfattning

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.
Originalspråkengelska
Titel på värdpublikationOperator Theory Advances and Applications (Operator Methods in Mathematical Physics, Conference on Operator Theory, Analysis and Mathematical Physics (OTAMP) 2010, Bedlewo, Poland)
RedaktörerJan Janas, Pavel Kurasov, Ari Laptev, Sergey Naboko
FörlagBirkhäuser Verlag
Sidor43-55
Antal sidor13
Volym227
ISBN (tryckt)978-3-0348-0531-5, 978-3-0348-0530-8 (print)
DOI
StatusPublished - 2013
Externt publiceradJa
EvenemangFifth International Conference on Operator Theory Analysis and Mathematical Physics (OTAMP 2010) - Bedlewo, Polen
Varaktighet: 2010 aug. 52010 aug. 12

Publikationsserier

Namn
Volym227
ISSN (tryckt)0255-0156
ISSN (elektroniskt)2296-4878

Konferens

KonferensFifth International Conference on Operator Theory Analysis and Mathematical Physics (OTAMP 2010)
Land/TerritoriumPolen
OrtBedlewo
Period2010/08/052010/08/12

Ämnesklassifikation (UKÄ)

  • Matematik

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