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

Bourget, A.; Goode, T.

doi:10.1090/proc/12658

Density of states of Jacobi matrices with periodic and asymptotically periodic coefficients
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by A. Bourget and T. M. Goode PDF

Proc. Amer. Math. Soc. 143 (2015), 5293-5306 Request permission

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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