P., Mathai, V., Schick, T. and Yates, S.: Approximating Spectral invariants of Harper operators on graphs II.
- Autor: Mathai Varghese,
Thomas Schick, Stuart Yates
- Titel: Approximating Spectral invariants of Harper operators on graphs II.
(dvi) (pdf)
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Proc. Am. Math. Soc. 131, No.6, 1917-1923 (2003), www.arXiv.org/math.SP/0201127
Abstract:
We study Harper operators and the closely related
discrete magnetic Laplacians (DML) on a graph with a free action
of a discrete group, as defined by Sunada \cite{Sun}.
The spectral density function of the DML is defined using the
von Neumann trace associated with the free action of a
discrete group on a graph. The main result in this paper states
that when the group is amenable, the spectral density function is equal to
the integrated density of states of the DML that is defined using either
Dirichlet or Neumann boundary conditions. This establishes the main
conjecture in \cite{MY}. The result is generalized to other self
adjoint operators with finite propagation speed.
Thomas Schick