Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

On the spectrum of the periodic Dirac operator

B. J. Harrisa1

a1 Department of Pure Mathematics, University College, Cardiff

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.

(Received June 03 1980)

(Revised October 17 1980)