This paper describes the connection between scattering matrices on conformally compact asymptotically Einstein manifolds and conformally invariant objects on their boundaries at infinity. Thisâ€¦ (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 quantumâ€¦ (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-cotensorâ€¦ (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 phaseâ€¦ (More)

(1.1) P (h) = âˆ’hâˆ† + V (x) , V âˆˆ Câˆž 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.â€¦ (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 hyperbolicâ€¦ (More)

We give a new upper bound on the Selberg zeta function for a convex co-compact Schottky group acting on the hyperbolic space H: in strips parallel to the imaginary axis the zeta function is boundedâ€¦ (More)