On the structure of spectra of periodic elliptic operators

Kuchment, Peter; Levendorskiî, Sergei

doi:10.1090/S0002-9947-01-02878-1

On the structure of spectra of periodic elliptic operators
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by Peter Kuchment and Sergei Levendorskiî PDF

Trans. Amer. Math. Soc. 354 (2002), 537-569 Request permission

Abstract:

The paper discusses the problem of absolute continuity of spectra of periodic elliptic operators. A new result on absolute continuity for a matrix operator of Schrödinger type is obtained. It is shown that all types of operators for which the absolute continuity has previously been established can be reduced to this one. It is also discovered that some natural generalizations stumble upon an obstacle in the form of non-triviality of a certain analytic bundle on the two-dimensional torus.

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