Bethe-Sommerfeld conjecture for periodic operators with strong perturbations

• 成果类型: Article
• 署名作者: Parnovski, Leonid; Sobolev, Alexander V.
• 署名单位: University of London; University College London
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-010-0251-1
• 发表日期: 2010
• 页码: 467-540
• 关键词: density-of-states; schrodinger operator; polyharmonic operator; eigenvalues; spectrum

摘要

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.