On some analytical index formulas related to operator-valued symbols.
On spectra of geometric operators on open manifolds and differentiable groupoids.
On super (or pseudo) differential forms as superfunctions
On the -singularities of regular holonomic distributions
The analytic and wave-front sets of a distribution which is a solution of a regular holonomic differential system are shown to coincide. More generally, we give comparison theorems for solutions of a regular holonomic system of microdifferential equations in various spaces of microfunctions, as a simple extension of a result of Kashiwara.
On the construction of fundamental solutions for differential operators on nilpotent groups
On the Fefferman-Phong inequality
We show that the number of derivatives of a non negative 2-order symbol needed to establish the classical Fefferman-Phong inequality is bounded by improving thus the bound obtained recently by N. Lerner and Y. Morimoto. In the case of symbols of type , we show that this number is bounded by ; more precisely, for a non negative symbol , the Fefferman-Phong inequality holds if are bounded for, roughly, . To obtain such results and others, we first prove an abstract result which says that...
On the geometry of Riemannian manifolds with a Lie structure at infinity.
On the index of nonlocal elliptic operators for compact Lie groups
We consider a class of nonlocal operators associated with a compact Lie group G acting on a smooth manifold. A notion of symbol of such operators is introduced and an index formula for elliptic elements is obtained. The symbol in this situation is an element of a noncommutative algebra (crossed product by G) and to obtain an index formula, we define the Chern character for this algebra in the framework of noncommutative geometry.
On the inversion of pseudo-differential operators
On the Laguerre calculus of left-invariant convolution (pseudo-differential) operators on the Heisenberg group
On trace theorems for pseudo-differential operators
Opérateurs à bicaractéristiques périodiques
Opérateurs différentiels hypoelliptiques et groupes nilpotents
Opérateurs pseudo-différentiels et asymptotique sur des variétés à singularités
Opérateurs pseudodifférentiels et représentations unitaires des groupes de Lie
Operatori pseudo-differenziali anisotropi su varietà fogliettate
Oscillatory integrals associated to folding canonical relations
Paramétrix d’opérateurs elliptiques de classe
Paramétrix pour un problème de Cauchy hyperbolique à multiplicité variable
Problemi di risolubilità di operatori differenziali invarianti sul gruppo di Heisenberg