Compositions of pseudo-differential operators
Conjoint spectral asymptotics for the families of commuting operators and for operators with the periodic hamiltonian flow
Construction de solutions nulles et singulières pour des opérateurs de type principal
Construction d'un inverse et propagation de la régularité des solutions pour un problème de Dirichlet hyperbolique
Construction of Sobolev spaces of fractional order with sub-riemannian vector fields
Given a smooth family of vector fields satisfying Chow-Hörmander’s condition of step 2 and a regularity assumption, we prove that the Sobolev spaces of fractional order constructed by the standard functional analysis can actually be “computed” with a simple formula involving the sub-riemannian distance.Our approach relies on a microlocal analysis of translation operators in an anisotropic context. It also involves classical estimates of the heat-kernel associated to the sub-elliptic Laplacian.
Contribution of noncommutative geometry to index theory on singular manifolds
This survey of the work of the author with several collaborators presents the way groupoids appear and can be used in index theory. We define the general tools, and apply them to the case of manifolds with corners, ending with a topological index theorem.
Contrôle et stabilisation pour l'équation des ondes
Convergence dans le domaine complexe des séries de fonctions propres
Correction to "Composition and L²-boundedness of flag kernels" (Colloq. Math. 118 (2010), 581-585)
Cutting the loss of derivatives for solvability under condition
For a principal type pseudodifferential operator, we prove that condition implies local solvability with a loss of 3/2 derivatives. We use many elements of Dencker’s paper on the proof of the Nirenberg-Treves conjecture and we provide some improvements of the key energy estimates which allows us to cut the loss of derivatives from for any (Dencker’s most recent result) to 3/2 (the present paper). It is already known that condition doesnotimply local solvability with a loss of 1 derivative,...