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On the spectrum of periodic elliptic operators

Published online by Cambridge University Press:  22 January 2016

Jochen Brüning  and
Toshikazu Sunada
Jochen Brüning
Affiliation:
Institut für Mathematik, Universität Augsburg, D-8900 Augsburg, BRD
Toshikazu Sunada
Affiliation:
Department of Mathematics, University of Tokyo, 113 Tokyo, Japan
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It was observed in [Su5] that the spectrum of a periodic Schrödinger operator on a Riemannian manifold has band structure if the transformation group acting on the manifold satisfies the Kadison property (see below for the definition). Here band structure means that the spectrum is a union of mutually disjoint, possibly degenerate closed intervals, such that any compact subset of R meets only finitely many. The purpose of this paper is to show, by a slightly different method, that this is also true for general periodic elliptic self-adjoint operators.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 126 , June 1992 , pp. 159 - 171
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1992

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