Sharp asymptotics of the quasimomentum

Details Sharp asymptotics of the quasimomentum Sharp asymptotics of the quasimomentum

2011-10-21

arxiv.org/abs/1110.4716v1

Mathematics

Spectral Theory

16 pages, 3 figures, keywords: quasimomentum, integrated density of states, periodic potential

Scientific paper

We consider the Schr\"odinger operator with a periodic potential $p$ on the
real line. We assume that $p$ belongs to the Sobolev space $\mH_m$ on the
circle for some $m\ge -1$, and we determine the asymptotics of the
quasimomentum and the Titchmarsh-Weyl functions, the Bloch functions at high
energy.

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