Laplace transform of Laplace hyperfunctions and its applications.
Les équations de Hua d'un domaine borné symétrique du type tube.
L'involutivité des caractéristiques des systèmes différentiels et microdifférentiels
Local Operators Between Spaces of Ultradifferentiable Functions and Ultradistributions.
Localizations of partial differential operators and surjectivity on real analytic functions
Let P(D) be a partial differential operator with constant coefficients which is surjective on the space A(Ω) of real analytic functions on an open set . Then P(D) admits shifted (generalized) elementary solutions which are real analytic on an arbitrary relatively compact open set ω ⊂ ⊂ Ω. This implies that any localization of the principal part is hyperbolic w.r.t. any normal vector N of ∂Ω which is noncharacteristic for . Under additional assumptions must be locally hyperbolic.
Microfunctions with values in a Clifford algebra 1
Microlocal properties of ultradistributions. Composition and kernel type operators.
Non-solvability of the tangential -systems
We prove that for a real analytic generic submanifold of whose Levi-form has constant rank, the tangential -system is non-solvable in degrees equal to the numbers of positive and negative Levi-eigenvalues. This was already proved in [1] in case the Levi-form is non-degenerate (with non-necessarily real analytic). We refer to our forthcoming paper [7] for more extensive proofs.
On a limit at infinity notion of an ultradistribution. (Sur une notion de limite à l'infini d'une ultradistribution.)
On complex interpolation with an analytic functional.
On the diametral dimension of weighted spaces of analytic germs
We prove precise estimates for the diametral dimension of certain weighted spaces of germs of holomorphic functions defined on strips near ℝ. This implies a full isomorphic classification for these spaces including the Gelfand-Shilov spaces and for α > 0. Moreover we show that the classical spaces of Fourier hyperfunctions and of modified Fourier hyperfunctions are not isomorphic.
On the range of convolution operators on non-quasianalytic ultradifferentiable functions
Let denote the non-quasianalytic class of Beurling type on an open set Ω in . For the surjectivity of the convolution operator is characterized by various conditions, e.g. in terms of a convexity property of the pair and the existence of a fundamental solution for μ or equivalently by a slowly decreasing condition for the Fourier-Laplace transform of μ. Similar conditions characterize the surjectivity of a convolution operator between ultradistributions of Roumieu type whenever . These...
Periodic Boehmians.
P-Functionale und Randwerte zu Hypoelliptischen Differentialoperatoren.
Plane waves, biregular functions and hypercomplex Fourier analysis
Polya's theorem for non-entire functions
Problèmes d'interpolation dans quelques espaces de fonctions non entières
Projective representations of spaces of quasianalytic functionals
The weighted inductive limit of Fréchet spaces of entire functions in N variables which is obtained as the Fourier-Laplace transform of the space of analytic functionals on an open convex subset of can be described algebraically as the intersection of a family of weighted Banach spaces of entire functions. The corresponding result for the spaces of quasianalytic functionals is also derived.
Propagation des singularités analytiques pour les solutions des équations aux dérivées partielles
Propagation of Holomorphic Extendability of CR Functions.