Analyse microlocale et équations d’évolution
Analytic hypoellipticity and local solvability for a class of pseudo-differential operators with symplectic characteristics
Analytic Hypo-Ellipticity and Propagation of Regularity for a System of Microdifferential Equations with Non-Involutory Characteristics.
Analytic index formulas for elliptic corner operators
Spaces with corner singularities, locally modelled by cones with base spaces having conical singularities, belong to the hierarchy of (pseudo-) manifolds with piecewise smooth geometry. We consider a typical case of a manifold with corners, the so-called "edged spindle", and a natural algebra of pseudodifferential operators on it with special degeneracy in the symbols, the "corner algebra". There are three levels of principal symbols in the corner algebra, namely the interior,...
Analyticité microlocale et itères d'opérateurs
Analyticité précisée d'opérateurs intégraux
Anisotropic classes of homogeneous pseudodifferential symbols
We define homogeneous classes of x-dependent anisotropic symbols in the framework determined by an expansive dilation A, thus extending the existing theory for diagonal dilations. We revisit anisotropic analogues of Hörmander-Mikhlin multipliers introduced by Rivière [Ark. Mat. 9 (1971)] and provide direct proofs of their boundedness on Lebesgue and Hardy spaces by making use of the well-established Calderón-Zygmund theory on spaces of homogeneous type. We then show that x-dependent symbols in...
Appendice à l'exposé : «Weak bloch property and weight estimates for elliptic operators»
Application de la théorie des microfonctions holomorphes au problème de Cauchy à données singulières
Applications of Fourier integral operators
Approximation by generalized impedance boundary conditions of a transmission problem in acoustic scattering
This paper addresses some results on the development of an approximate method for computing the acoustic field scattered by a three-dimensional penetrable object immersed into an incompressible fluid. The basic idea of the method consists in using on-surface differential operators that locally reproduce the interior propagation phenomenon. This approach leads to integral equation formulations with a reduced computational cost compared to standard integral formulations coupling both the transmitted...
Approximation by generalized impedance boundary conditions of a transmission problem in acoustic scattering
This paper addresses some results on the development of an approximate method for computing the acoustic field scattered by a three-dimensional penetrable object immersed into an incompressible fluid. The basic idea of the method consists in using on-surface differential operators that locally reproduce the interior propagation phenomenon. This approach leads to integral equation formulations with a reduced computational cost compared to standard integral formulations coupling both the transmitted...
Approximation des systèmes d'opérateurs pseudodifférentiels
Approximation of Pseudodifferential Operators in Absorbing Boundary Conditions for Hyperbolic Equations.
Approximation semi-classique de l'équation de Heisenberg
Aproximación clásica de la ecuación de Dirac cuando
Around 3D Boltzmann non linear operator without angular cutoff, a new formulation
Around 3D Boltzmann non linear operator without angular cutoff, a new formulation
We propose a new formulation of the 3D Boltzmann non linear operator, without assuming Grad's angular cutoff hypothesis, and for intermolecular laws behaving as 1/rs, with s> 2. It involves natural pseudo differential operators, under a form which is analogous to the Landau operator. It may be used in the study of the associated equations, and more precisely in the non homogeneous framework.
Asymptotic behavior of the spectrum of singular Green operators
Asymptotics for Bergman kernels for high powers of complex line bundles, based on joint works with B. Berndtsson and R. Berman
Nous discutons l’asymptotique des noyaux de Bergman pour des puissances élevées de fibrés de droites, d’après deux travaux récents avec B.Berndtsson et R. Berman.