On the structure of spectra of periodic elliptic operators
نویسندگان
چکیده
منابع مشابه
On the Structure of Spectra of Periodic Elliptic Operators
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 ob...
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15 صفحه اولOn absolute continuity of spectra of periodic elliptic operators
The paper contains a brief description of a simplified version of A. Sobolev’s proof of absolute continuity of spectra of periodic magnetic Schrödinger operators. This approach is applicable to all periodic elliptic operators known to be of interest for math physics (including Maxwell), and in all these cases leads to the same model problem of complex analysis. The full account of this approach...
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On the Spectrum of Periodic Elliptic Operators
It was observed in [Su5] that the spectrum of a periodic Schrodinger operator on a Riemannian manifold has band structure if the transformation group acting on the manifold satisfies the Kadison property (see below for the definition). Here band structure means that the spectrum is a union of mutually disjoint, possibly degenerate closed intervals, such that any compact subset of R meets only f...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2001
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-01-02878-1