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asymptotics of generalized eigenvectors

Proceedings of the Edinburgh Mathematical Society (1)

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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
Serguei Naboko, Sergey Simonov
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 53 / Issue 1 / February 2010

Published online by Cambridge University Press:

12 January 2010, pp. 239-254
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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.