Bethe-Sommerfeld conjecture for pseudodifferential perturbation

Details Bethe-Sommerfeld conjecture for pseudodifferential perturbation Bethe-Sommerfeld conjecture for pseudodifferential perturbation

2008-04-22

arxiv.org/abs/0804.3488v2

Mathematics

Spectral Theory

33 pages; misprints corrected; to appear in CPDE

Scientific paper

We consider a periodic pseudodifferential operator $H=(-\Delta)^l+A$ ($l>0$)
in $\R^d$ which satisfies the following conditions: (i) the symbol of $H$ is
smooth in $x$, and (ii) the perturbation $A$ has order smaller than $2l-1$.
Under these assumptions, we prove that the spectrum of $H$ contains a
half-line.

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