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On the spectrum of the periodic Dirac operator

  • B. J. Harris (a1)

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.

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1 F. V. Atkinson . A spectral problem for completely continuous operators. Acta Math. Acad. Sci. Hungar. 3 (1952), 5360.

5 W. D. Evans . Spectral theory of the Dirac operator. Math. Z. 121 (1971), 123.

7 T. Kato . Perturbation theory for linear operators (Berlin: Springer, 1966).

8 U. V. Schminke . A spectral gap theorem for Dirac operators with central field. Math. Z. 131 (1973), 351356.

9 L. E. Thomas . Time dependent approach to scattering from impurities in a crystal. Comm. Math. Phys. 33 (1973), 335343.

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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