Asymptotics of the integrated density of states for periodic elliptic pseudo-differential operators in dimension one

DOI10.4171/RMI/449zbMath1121.35149OpenAlexW2024754535MaRDI QIDQ854545

Alexander V. Sobolev

Publication date: 5 December 2006

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/41965

zbMATH Keywords

spectral theorydensity of statesSchrödinger type operators

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Perturbation theory of linear operators (47A55) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Pseudodifferential operators (47G30)

Related Items (9)

Complete asymptotic expansions of the spectral function for symbolic perturbations of almost periodic Schrödinger operators in dimension one ⋮ Complete Semiclassical Spectral Asymptotics for Periodic and Almost Periodic Perturbations of Constant Operators ⋮ Classical wave methods and modern gauge transforms: spectral asymptotics in the one dimensional case ⋮ 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 ⋮ Complete asymptotic expansion of the integrated density of states of multidimensional almost-periodic pseudo-differential operators ⋮ Bethe-Sommerfeld conjecture for periodic operators with strong perturbations ⋮ An overview of periodic elliptic operators ⋮ Integrated density of states: From the finite range to the periodic Airy–Schrödinger operator

Cites Work

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• Perturbation theory for the Schrödinger operator with a periodic potential
• Lattice points, perturbation theory and the periodic polyharmonic operator.

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