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Group C*-Algebras and the Spectrum of a Periodic Schrödinger Operator on a Manifold

Published online by Cambridge University Press:  20 November 2018

Toshikazu Sunada
Toshikazu Sunada*
Affiliation:
Department of Mathematics, Nagoya University, Nagoya 464, Japan
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The spectrum of the Laplacian or more generally of a Schrödinger operator on an open manifold may have possibly a complicated aspect. For example, a Cantor set in the real axis may appear as the spectrum even for an innocent looking potential on a standard Riemannian manifold (see J. Moser [10]). The fundamental result of the spectral theory of periodic Schrödinger operators, however, says that the picture of the spectrum of a Schrödinger operator on ℝn with a periodic potential is simple; indeed the spectrum consists of a series of closed intervals of the real axis without accumulation, separated in general by gaps outside the spectrum (see M. Reed and B. Simon [13] or M. M. Skriganov [15] for instance).

Keywords

58G2547C15
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 1 , 01 December 1991 , pp. 180 - 193
Copyright
Copyright © Canadian Mathematical Society 1989

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