Search results

Search: All articles in the CJM digital archive with keyword scattering theory

 Expand all        Collapse all Results 1 - 2 of 2

1. CJM 2011 (vol 63 pp. 961)

Bouclet, Jean-Marc
 Low Frequency Estimates for Long Range Perturbations in Divergence Form We prove a uniform control as $z \rightarrow 0$ for the resolvent $(P-z)^{-1}$ of long range perturbations $P$ of the Euclidean Laplacian in divergence form by combining positive commutator estimates and properties of Riesz transforms. These estimates hold in dimension $d \geq 3$ when $P$ is defined on $\mathbb{R}^d$ and in dimension $d \geq 2$ when $P$ is defined outside a compact obstacle with Dirichlet boundary conditions. Keywords:resolvent estimates, thresholds, scattering theory, Riesz transformCategory:35P25

2. CJM 2000 (vol 52 pp. 897)

Christiansen, T. J.; Joshi, M. S.
 Higher Order Scattering on Asymptotically Euclidean Manifolds 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 integral operator associated to the geodesic flow at time $\pi$ on the boundary. Furthermore, it is shown that on $\Real^n$ the asymptotics of certain short-range perturbations of $\Delta^k$ can be recovered from the scattering matrix at a finite number of energies. Keywords:scattering theory, conormal, LagrangianCategory:58G15