Weighted spectral gap for magnetic Schrödinger operator with a potential term

Inverse Problem for Interior Spectral Data of the Dirac Operator with Discontinuous Conditions

In this paper, we study the inverse problem for Dirac differential operators with  discontinuity conditions in a compact interval. It is shown that the potential functions can be uniquely determined by the value of the potential on some interval and parts of two sets of eigenvalues. Also, it is shown that the potential function can be uniquely determined by a part of a set of values of eigenfun...

Semiclassical Spectral Invariants for Schrödinger Operators

In this article we show how to compute the semi-classical spectral measure associated with the Schrödinger operator on Rn, and, by examining the first few terms in the asymptotic expansion of this measure, obtain inverse spectral results in one and two dimensions. (In particular we show that for the Schrödinger operator on R2 with a radially symmetric electric potential, V , and magnetic potent...

Semiclassical Spectral Asymptotics for a Two–Dimensional Magnetic Schrödinger Operator: The Case of Discrete Wells

Spectral Shift Function for Schrödinger Operators in Constant Magnetic Fields

We consider the three-dimensional Schrödinger operator with constant magnetic field, perturbed by an appropriate short-range electric potential, and investigate various asymptotic properties of the corresponding spectral shift function (SSF). First, we analyse the singularities of the SSF at the Landau levels. Further, we study the strong magnetic field asymptotic behaviour of the SSF; here we ...

On Spectral Analysis of a Magnetic Schrödinger Operator on Planar Mixed Automorphic Forms

We characterize the space of the so-called planar mixed automorphic forms of type (ν, μ) with respect to an equivariant pair (ρ, τ) as the image of the usual automorphic forms by an appropriate transform and we investigate some concrete basic spectral properties of a magnetic Schrödinger operator acting on them. The associated polynomials constitute classes of generalized complex polynomials of...