Bethe–Sommerfeld Conjecture for Pseudodifferential Perturbation

DOI10.1080/03605300902769006zbMath1185.35349arXiv0804.3488OpenAlexW2118632118MaRDI QIDQ5321926

Leonid Parnovski, Gerassimos Barbatis

Publication date: 16 July 2009

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0804.3488

zbMATH Keywords

periodic problemsspectral gapspseudo-differential operatorsBethe-Sommerfeld conjecture

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Pseudodifferential and Fourier integral operators on manifolds (58J40) Pseudodifferential operators (47G30)

Related Items (9)

On lacunas in the lower part of the spectrum of the periodic magnetic operator in a strip ⋮ The almost periodic gauge transform: an abstract scheme with applications to Dirac operators ⋮ Complete asymptotic expansion of the integrated density of states of multidimensional almost-periodic Schrödinger operators ⋮ On spectral gaps of a Laplacian in a strip with a bounded periodic perturbation ⋮ Bethe-Sommerfeld conjecture for periodic operators with strong perturbations ⋮ Absence of gaps in a lower part of the spectrum of a Laplacian with frequent alternation of boundary conditions in a strip ⋮ An overview of periodic elliptic operators ⋮ On lacunas in the spectrum of the Laplacian with the Dirichlet boundary condition in a band with oscillating boundary ⋮ Bethe-Sommerfeld conjecture for periodic Schrödinger operators in strip

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