This article is cited in 15 papers

Gauge-periodic point perturbations on the Lobachevsky plane

J. Brüning^a, V. A. Geiler<sup>b

a</sup> Humboldt University
^b Mordovian State University

Abstract: We study periodic point perturbations of the Shrödinger operator with a uniform magnetic field on the Lobachevsky plane. We prove that the spectrum gaps of the perturbed operator are labeled by the elements of the $K_0$ group of a $C^*$ algebra associated with the operator. In particular, if the $C^*$ algebra has the Kadison property, then the operator spectrum has a band structure.

Received: 23.07.1998
Revised: 15.01.1999

DOI: 10.4213/tmf745

 English version: Theoretical and Mathematical Physics, 1999, 119:3, 687–697

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