Department Mathematik
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Dr. Sergey Morozov

Mathematisches Institut der Universität München
Theresienstr. 39
D-80333 München

Email: morozov@math.lmu.de

Tel:   +49 (0)89   2180 4613
Büro: Block B, 4. Stock, 413

Arbeitsgruppe Analysis
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Spectraltheorie periodischer Operatoren

Lectures: Mo 14-16, B 251
Exercises: Mo 16-18, B 251

The course is devoted to the study of spectral properties of self-adjoint operators commuting with translations in one or several dimensions. We will start from the Floquet-Bloch theory which allows to decompose such operators into direct integrals and deduce the band structure of their spectra. Then we will study the behavior of the band functions for particular classes of models and discuss the questions of absolute continuity of their spectra, location and absence of spectral gaps, overlapping of the band functions and the behavior of the density of states.