Scattering matrix for asymptotically euclidean manifolds
Scattering on stratified media: the microlocal properties of the scattering matrix and recovering asymptotics of perturbations
The scattering matrix is defined on a perturbed stratified medium. For a class of perturbations, its main part at fixed energy is a Fourier integral operator on the sphere at infinity. Proving this is facilitated by developing a refined limiting absorption principle. The symbol of the scattering matrix determines the asymptotics of a large class of perturbations.
Semigroup commutators under differences (II).
This is the second instalment of my previous paper with the same title, [1]. This paper consists of two different parts. The first part is devoted to improvements of the results developed in [1]. These improvements are described in section 0.1 below and developed in sections 1 to 5, and 9 to 10; they are in fact technically distinct from [1] and rely on a systematic use of microlocalisation in the context of Hörmander-Weyl calculus. These paragraphs can therefore be read quite independently from...
Semilinear waves with cusp singularities
Sheaf theory and regularity. Application to local and microlocal analysis
A review of some methods in sheaf theory is presented to make precise a general concept of regularity in algebras or spaces of generalized functions. This leads to the local analysis of the sections of sheaves or presheaves under consideration and then to microlocal analysis and microlocal asymptotic analysis.
Singularités des solutions d'équations d'ondes semi-linéaires
Slopes of hypergeometric systems of codimension one.
We describe the slopes, with respect to the coordinates hyperplanes, of the hypergeometric systems of codimension one, that is when the toric ideal is generated by one element.
Smoothing of dispersive waves
Stabilization of Schrödinger equation in exterior domains
We prove uniform local energy estimates of solutions to the damped Schrödinger equation in exterior domains under the hypothesis of the Exterior Geometric Control. These estimates are derived from the resolvent properties.