Adjoints of elliptic boundary value problems
An accuracy improvement in Egorov's theorem.
We prove that the theorem of Egorov, on the canonical transformation of symbols of pseudodifferential operators conjugated by Fourier integral operators, can be sharpened. The main result is that the statement of Egorov's theorem remains true if, instead of just considering the principal symbols in Sm/Sm-1 for the pseudodifferential operators, one uses refined principal symbols in Sm/Sm-2, which for classical operators correspond simply to the principal plus the subprincipal symbol, and can generally...
Analogue d'un Lemme de Kohn et Nirenberg
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.
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»
Applications of Fourier integral operators
Approximation des systèmes d'opérateurs pseudodifférentiels
Approximation semi-classique de l'équation de Heisenberg
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.
Asymptotics of the integrated density of states for periodic elliptic pseudo-differential operators in dimension one.
We consider a periodic pseudo-differential operator on the real line, which is a lower-order perturbation of an elliptic operator with a homogeneous symbol and constant coefficients. It is proved that the density of states of such an operator admits a complete asymptotic expansion at large energies. A few first terms of this expansion are found in a closed form.
Asymptotique de la phase de diffusion à haute énergie pour l'opérateur de Dirac