Victor Ivrii: Complete Spectral Asymptotics for Periodic and Almost Periodic Perturbations of Constant Operators and Bethe-Sommerfeld Conjecture in Semiclassical Settings

Under certain assumptions we derive a complete semiclassical asymptotics of a spectral function of the constant coefficient scalar operator perturbed by almost periodic “smaller” operator.In particular, a complete semiclassical asymptotics of the integrated density of states also holds.
Under similar assumptions for periodic perturbations Bethe-Sommerfeld conjecture in semiclassical settings holds.