Abstract

On spectra of periodic operators A. Sobolev Spectra of periodic operators are known to consist of a collection of non-intersecting closed intervals called bands, separated by spectrum-free intervals called gaps. More detailed information can be obtained for concrete examples. The talk will address the properties of the periodic Schr\"odinger operator. The following two burning questions will be discussed: Do spectral bands degenerate into points? Is the number of gaps finite or infinite? Study of these questions is an important mathematical and physical issue involving a versatile arsenal of methods. The aim of the talk is to review old results and recent developments in the field.

General Enquiries Dr. Malcolm Brown. Computer Science Cardiff University PO Box 916 Cardiff CF24 3XF, U.K. Malcom@cs.cf.ac.uk

N.B. All Mathematics appears in TeX/LaTeX source.

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