Density of states of Jacobi matrices with periodic and asymptotically periodic coefficients
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- by A. Bourget and T. M. Goode PDF
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Abstract:
The paper is concerned with Jacobi matrices having periodic or asymptotically periodic coefficients. In the first part, we give an elementary derivation of the well-known density of states of Jacobi matrices with periodic coefficients; our approach is independent from the standard arguments using Floquet theory or potential theory. In the last part of the paper, we extend the results of Van Assche, published in 1999, on Jacobi matrices with asymptotically periodic coefficients depending on a parameter.References
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Additional Information
- A. Bourget
- Affiliation: Department of Mathematics, McCarthy Hall 154, California State University (Fullerton), Fullerton, California 92834
- Email: abourget@fullerton.edu
- T. M. Goode
- Affiliation: Department of Mathematics, McCarthy Hall 154, California State University (Fullerton), Fullerton, California 92834
- Received by editor(s): July 14, 2013
- Received by editor(s) in revised form: October 2, 2014
- Published electronically: June 3, 2015
- Communicated by: Walter Van Assche
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 5293-5306
- MSC (2010): Primary 47B36, 34L20
- DOI: https://doi.org/10.1090/proc/12658
- MathSciNet review: 3411147