Titlebook: Microlocal Analysis, Sharp Spectral Asymptotics and Applications V; Applications to Quan Victor Ivrii Book 2019 Springer Nature Switzerland

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The Case of External Magnetic FieldIn this Chapter we repeat analysis of the previous Chapter . but in the case of the constant external magnetic field

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The Case of Combined Magnetic FieldIn this Chapter instead of the Schrödinger operator without magnetic field as in Chapter ., or with a constant magnetic field as in Chapter ., or with a self-generated magnetic field as in Chapter 

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Spectral Asymptotics for Dirichlet to Neumann Operator in the Domains with EdgesWe consider eigenvalues of the Dirichlet-to-Neumann operator for Laplacian in the domain (or manifold) with edges and establish the asymptotics of the eigenvalue counting function . where . is dimension of the boundary. Further, in certain cases we establish two-term asymptotics . We also establish improved asymptotics for Riesz means.

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Bethe-Sommerfeld Conjecture in Semiclassical SettingsUnder certain assumptions (including . we prove that the spectrum of a scalar operator in .covers interval ., where . is an elliptic operator and .(., .) is a periodic perturbation, ., .. .Further, we consider generalizations.