Journal
INVENTIONES MATHEMATICAE
Volume 181, Issue 3, Pages 467-540Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00222-010-0251-1
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Funding
- EPSRC [EP/F029721/1, EP/D00022X/2]
- Leverhulme
- EPSRC [EP/D00022X/2, EP/F029721/1, EP/D00022X/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/F029721/1, EP/D00022X/2, EP/D00022X/1] Funding Source: researchfish
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We consider a periodic self-adjoint pseudo-differential operator H=(-Delta) (m) +B, m > 0, in ae (d) which satisfies the following conditions: (i) the symbol of B is smooth in x, and (ii) the perturbation B has order less than 2m. Under these assumptions, we prove that the spectrum of H contains a half-line. This, in particular implies the Bethe-Sommerfeld conjecture for the Schrodinger operator with a periodic magnetic potential in all dimensions.
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