Sur une classe d'opérateurs de type sous-elliptique
Sur une classe d'opérateurs pseudodifférentiels hypoelliptiques à caractéristiques doubles, d'après L. Hörmander
Symbol calculus on the affine group "ax + b"
The symbol calculus on the upper half plane is studied from the viewpoint of the Kirillov theory of orbits. The main result is the -estimates for Fuchs type pseudodifferential operators.
Symétrisations indépendantes du temps pour certains opérateurs du type de Schrödinger. I
Si danno condizioni sufficienti e condizioni necessarie affinché il problema di Cauchy per alcuni operatori di tipo Schrödinger sia ben posto in spazi di Sobolev. Gli operatori qui considerati sono operatori di Schrödinger con potenziali vettoriali complessi, una generalizzazione degli operatori di 2-evoluzione nel senso di Petrowsky, e alcuni sistemi tipo Leray-Volevich di operatori lineari a derivate parziali. Il metodo che usiamo in questo articolo è la simmetrizazione degli operatori non dipendenti...
Symplectic classification of quadratic forms, and general Mehler formulas.
Système sous-elliptiques II.
Systèmes micro-hyperboliques
Systèmes sous-elliptiques
Systems of meromorphic microdifferential equations
We introduce the notion of system of meromorphic microdifferential equations. We use it to prove a desingularization theorem for systems of microdifferential equations.
The Cauchy problem for degenerate parabolic equations in Gevrey classes
The Cauchy problem for one class of parabolic pseudodifferential systems with nonsmooth symbols.
The convergence estimates for Galerkin-wavelet solution of periodic pseudodifferential initial value problems.
The density of the area integral in
Let be a harmonic function in the half-plane , . We define a family of functionals , that are analogs of the family of local times associated to the process where is Brownian motion in . We show that is bounded in if and only if belongs to , an equivalence already proved by Barlow and Yor for the supremum of the local times. Our proof relies on the theory of singular integrals due to Caldéron and Zygmund, rather than the stochastic calculus.
The Essential Spectrum of Elliptic Systems of Mixed Order.
The Fast Fourier Transform and the Numerical Solution of One-Dimensional Boundary Integral Equations.
The Fourier integral operators on Hardy spaces associated with Herz spaces
In this paper, it is proved that the Fourier integral operators of order , with , are bounded from three kinds of Hardy spaces associated with Herz spaces to their corresponding Herz spaces.
The geometric optics for a class of hyperbolic second order operators with Hölder continuous coefficients with respect to time
The level crossing problem in semi-classical analysis I. The symmetric case
We describe a microlocal normal form for a symmetric system of pseudo-differential equations whose principal symbol is a real symmetric matrix with a generic crossing of eigenvalues. We use it in order to give a precise description of the microlocal solutions.
The level crossing problem in semi-classical analysis. II. The Hermitian case
This paper is the second part of the paper ``The level crossing problem in semi-classical analysis I. The symmetric case''(Annales de l'Institut Fourier in honor of Frédéric Pham). We consider here the case where the dispersion matrix is complex Hermitian.
The microlocal Landau-Zener formula