Extensions du théorème de Holmgren
Extrapolation pour les mesures de Carleson et conjecture de Kato
Factorisation d'opérateurs différentiels à coefficients rationnels
Failure of analytic hypoellipticity in a class of differential operators
For the hypoelliptic differential operators introduced by T. Hoshiro, generalizing a class of M. Christ, in the cases of and left open in the analysis, the operators also fail to be analytic hypoelliptic (except for ), in accordance with Treves’ conjecture. The proof is constructive, suitable for generalization, and relies on evaluating a family of eigenvalues of a non-self-adjoint operator.
Faisceaux d'espaces de Sobolev et principes du minimum
On montre que le faisceau des sursolutions locales dans d’un certain opérateur elliptique est maximal pour un principe du minimum adapté aux espaces de Sobolev. La continuité de la réduite variationnelle des éléments continus permet alors d’étudier des représentants s.c.i.
Finite eigenfunction approximations for continuous spectrum operators.
Flot hamiltonien et spectre d'un opérateur elliptique
Fonction spectrale d'opérateurs non elliptiques
Formes bilinéaires compatibles avec un système hyperbolique et problème de Cauchy
Fourier-Wigner transforms and Liouville's theorems for the sub-Laplacian on the Heisenberg group
The sub-Laplacian on the Heisenberg group is first decomposed into twisted Laplacians parametrized by Planck's constant. Using Fourier-Wigner transforms so parametrized, we prove that the twisted Laplacians are globally hypoelliptic in the setting of tempered distributions. This result on global hypoellipticity is then used to obtain Liouville's theorems for harmonic functions for the sub-Laplacian on the Heisenberg group.
Fredholm properties of elliptic operators on ℝⁿ [Book]
Fredholm property for a parameter dependent second order operator differential equation.
Garding's inequality for elliptic differential operator with infinite number of variables.
Ger-type and Hyers--Ulam stabilities for the first-order linear differential operators of entire functions.
Global solutions of semilinear heat equations in Hilbert spaces.
Green's function and convergence of Fourier series for elliptic differential operators with potential from Kato space.
Group Actions on the Solutions of Linear Partial Differential Equations.
functional calculus for an elliptic operator on a half-space with general boundary conditions
Let be the realization () of a differential operator on with general boundary conditions (). Here is a homogeneous polynomial of order in complex variables that satisfies a suitable ellipticity condition, and for is a homogeneous polynomial of order...
Hardy space H1 associated to Schrödinger operator with potential satisfying reverse Hölder inequality.
Let {Tt}t>0 be the semigroup of linear operators generated by a Schrödinger operator -A = Δ - V, where V is a nonnegative potential that belongs to a certain reverse Hölder class. We define a Hardy space HA1 by means of a maximal function associated with the semigroup {Tt}t>0. Atomic and Riesz transforms characterizations of HA1 are shown.
Hardy-type estimates for Dirac operators