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A discrete analogue of periodic magnetic Schrödinger operators. (English) Zbl 0805.47028

Brooks, Robert (ed.) et al., Geometry of the spectrum. 1993 joint summer research conference on spectral geometry, July 17-23, 1993, Univ. of Washington, Seattle, USA. Providence, RI: American Mathematical Society. Contemp. Math. 173, 283-299 (1994).
Summary: This paper presents a general method to investigate the spectrum of a graph-theoretical generalization of the classical Harper operators, a discretization of the Schrödinger operator with a uniform magnetic field. The generalized Harper operator is to be defined as a difference operator with a weak invariance property under a group action on a graph. Associated with such an operator is a twisted group \(C^*\)-algebra (the rotation algebra in the classical case) on which our method is founded. The continuous model, the Schrödinger operator on a manifold with a periodic magnetic field, is also discussed along the same idea.
For the entire collection see [Zbl 0801.00036].

MSC:

47B39 Linear difference operators
47F05 General theory of partial differential operators
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