This paper describes the connection between scattering matrices on conformally compact asymptotically Einstein manifolds and conformally invariant objects on their boundaries at infinity. This… (More)

The purpose of this article is to discuss a simple linear algebraic tool which has proved itself very useful in the mathematical study of spectral problems arising in elecromagnetism and quantum… (More)

Any compact C manifold with boundary admits a Riemann metric on its interior taking the form xdx + xh near the boundary, where x is a boundary defining function and h is a smooth symmetric 2-cotensor… (More)

We give pole free strips and estimates for resolvents of semiclassical operators which, on the level of the classical flow, have normally hyperbolic smooth trapped sets of codimension two in phase… (More)

The purpose of this note is to apply the methods of geometric scattering theory developed by Briet-Combes-Duclos [6], Gérard-Sjöstrand [14], Mazzeo-Melrose [22] and the second author [30] in the… (More)

(1.1) P (h) = −h∆ + V (x) , V ∈ C∞ c (X) , X = R , with hyperbolic classical flows, the smallness of dimension of the trapped set implies that there is a gap between the resonances and the real axis.… (More)

We present a wave group version of the Selberg trace formula for an arbitrary surface of nite geometry. As an application we give a new lower bound on the number of resonances for hyperbolic… (More)

We prove that for evolution problems with normally hyperbolic trapping in phase space, correlations decay exponentially in time. Normal hyperbolic trapping means that the trapped set is smooth and… (More)