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Spectral analysis of a class of hermitian Jacobi matrices in a critical (double root) hyperbolic case

Part of: Special classes of linear operators

Published online by Cambridge University Press:  12 January 2010

Serguei Naboko  and
Sergey Simonov
Serguei Naboko
Affiliation:
Department of Mathematics Physics, Institute of Physics, St Petersburg University, Ulianovskaia 1, St Petergoff, St Petersburg 198904, Russia, Email: ([email protected], [email protected])
Sergey Simonov
Affiliation:
Department of Mathematics Physics, Institute of Physics, St Petersburg University, Ulianovskaia 1, St Petergoff, St Petersburg 198904, Russia, Email: ([email protected], [email protected])
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Abstract

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We consider a class of Jacobi matrices with periodically modulated diagonal in a critical hyperbolic (‘double root’) situation. For the model with ‘non-smooth’ matrix entries we obtain the asymptotics of generalized eigenvectors and analyse the spectrum. In addition, we reformulate a very helpful theorem from a paper by Janas and Moszynski in its full generality in order to serve the needs of our method.

Keywords

Jacobi matricessubordinacy theoryasymptotics of generalized eigenvectors

MSC classification

Secondary: 47B36: Jacobi (tridiagonal) operators (matrices) and generalizations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 53 , Issue 1 , February 2010 , pp. 239 - 254
Copyright
Copyright © Edinburgh Mathematical Society 2010