An analytic FBI transform is built on compact manifolds without boundary, that satisfies all
the expected properties. It enables the study of microlocal analytic and Gevrey regularity on …

This paper present a synthesis concerning applications of Gaussian coher-ent states in semi-
classical analysis for Schrödinger type equations, time dependent or time independent. We …

Microlocal smoothing effect for the Schrödinger evolution equation in a Gevrey class Page 1
J. Math. Pures Appl. 91 (2009) 115–136 www.elsevier.com/locate/matpur Microlocal …

We prove exponentially small estimates on the off-diagonal terms of the scattering matrix
associated to two-state semiclassical Schrödinger Hamiltonians. Our method is based on …

Let H 0 be a self-adjoint operator in some Hilbert space H, and let λ 0 be a (possibly
degenerate) eigenvalue of H 0 embedded in its essential spectrum σ ess (H 0) with …

We develop a microlocal study for scalar classical analytic pseudo-differential operators of
principal type. Next, we reduce a system of pseudo-differential operators to the normal form …

The adiabatic theorem in quantum mechanics can be understood as an e ect of phase
space tunneling 12]. This allows us to use microlocal methods from the theory of pseudo di …

We study the Gevrey singularities of solutions of microhyperbolic equations using
exponential weighted estimates in the phase space. In particular, we recover some known …

We study the asymptotic properties of the Bergman kernels associated to tensor powers of a
positive line bundle on a compact K\" ahler manifold. We show that if the K\" ahler potential is …

We discuss the energy level splitting Δ epsilon due to quantum tunnelling between
congruent tori in phase space. In analytic cases, it is well known that Δ epsilon decays faster …