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Spectral properties of periodic pseudo-differential operators

Pchelintseva, I; (2012) Spectral properties of periodic pseudo-differential operators. Doctoral thesis , UCL (University College London). Green open access

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Abstract

We study elliptic diff erential and pseudo-differential operators with periodic coefficients. For a wide class of such operators we prove the Bethe-Sommerfeld conjecture, i.e. that the spectrum can have only finitely many gaps. We also study the integrated density of states of periodic Schroedinger operators and prove a lower bound for its variance in the high energy regime. This results in the lower bound for the non-integrated density of states of such operators.

Type: Thesis (Doctoral)
Title: Spectral properties of periodic pseudo-differential operators
Open access status: An open access version is available from UCL Discovery
Language: English
UCL classification: UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
URI: http://discovery.ucl.ac.uk/id/eprint/1357491
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