6 citations · 12 across the 4 of their papers we have counts for
6 papers
The resonance counting function for Schrödinger operators with generic potentials
T. Christiansen, P. D. Hislop
We show that the resonance counting function for a Schrödinger operator has maximal order of growth for generic sets of real-valued, or complex-valued, -compactly support…
Schrödinger operators with complex-valued potentials and no resonances
T. Christiansen
In dimension , we give examples of nontrivial, compactly supported, complex-valued potentials such that the associated Schrödinger operators have no resonances. If ,…
Asymptotics for a resonance-counting function for potential scattering on cylinders
T. Christiansen
We study certain resonance-counting functions for potential scattering on infinite cylinders or half-cylinders. Under certain conditions on the potential, we obtain asymptotics of…
Resonances for steplike potentials: forward and inverse results
T. Christiansen
We consider resonances associated to the operator , where if and if , with . We obtain asymptotics of t…
Scattering on stratified media: the micro-local properties of the scattering matrix and recovering asymptotics of perturbations
T. J. Christiansen, M. S. Joshi
The fixed energy scattering matrix is defined on a perturbed stratified medium, and for a class of perturbations, its main part is shown to be a Fourier integral operator on the sp…
Higher order scattering on asymptotically Euclidean Manifolds
T. J. Christiansen, M. S. Joshi
We develop a scattering theory for perturbations of powers of the Laplacian on asymptotically Euclidean manifolds. The (absolute) scattering matrix is shown to be a Fourier integra…