We study quantum scattering on manifolds equivalent to the Euclidean space near infinity, in
the semiclassical regime. We assume that the corresponding classical flow admits a non …

The limiting absorption principle asserts that if H is a suitable Schrödinger operator, and f
lives in a suitable weighted L 2 space (namely H^ 0, 1/2+ σ H 0, 1/2+ σ for some σ> 0 σ> 0) …

Abstract In Do, Doi proved that the L^ 2 _ t H^ 1/2 _ x local smoothing effect for Schrödinger
equations on a Riemannian manifold does not hold if the geodesic flow has one trapped …

We present an overview of mathematical results and methods relevant for the spectral study
of semiclassical Schrödinger (or wave) operators of scattering systems, in cases where the …

We prove a resolvent estimate for the Laplace-Beltrami operator on a scattering manifold
with a hyperbolic trapped set, and as a corollary deduce local smoothing. We use a result of …

We consider a family of surfaces of revolution, each with a single periodic geodesic which is
degenerately unstable. We prove a local smoothing estimate for solutions to the linear …

We prove resolvent estimates for semiclassical operators such as− h 2 Δ+ V (x) in scattering
situations. Provided the set of trapped classical trajectories supports a chaotic flow and is …

Let $\Omega\subset\mathbb {R}^ N $ be a compact imbedded Riemannian manifold of
dimension $ d\ge 1$ and define the $(d+ 1) $-dimensional Riemannian manifold $\mathcal …

We discuss recent progress in understanding the effects of certain trapping geometries on
cut-off resolvent estimates, and thus on the qualititative behavior of linear evolution …

In this thesis we study spectral properties of the Schrödinger operator on non compact
domains equipped with Riemannian metrics. More precisely, we are interested in the …