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On the spectrum of the periodic Dirac operator

Published online by Cambridge University Press:  14 November 2011

B. J. Harris
B. J. Harris
Affiliation:
Department of Pure Mathematics, University College, Cardiff
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Synopsis

In an earlier paper we considered periodic Dirac operators and obtained criteria for them to be self-adjoint and for their spectra to be devoid of eigenvalues of finite multiplicity. The question of the existence of eigenvalues of infinite multiplicity was left open. In this article we obtain further criteria for self-adjointness and show that under these conditions periodic Dirac operators do not possess eigenvalues of infinite multiplicity. We also obtain a spectral gap result.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 89 , Issue 1-2 , 1981 , pp. 55 - 62
Copyright
Copyright © Royal Society of Edinburgh 1981

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