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Density of states of Jacobi matrices with periodic and asymptotically periodic coefficients


Authors: A. Bourget and T. M. Goode
Journal: Proc. Amer. Math. Soc. 143 (2015), 5293-5306
MSC (2010): Primary 47B36, 34L20
DOI: https://doi.org/10.1090/proc/12658
Published electronically: June 3, 2015
MathSciNet review: 3411147
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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.


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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

DOI: https://doi.org/10.1090/proc/12658
Keywords: Jacobi matrices, spectrum, density of states
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
Article copyright: © Copyright 2015 American Mathematical Society

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