A distributional representation of strip analytic functions.
A general approximation theorem of Whitney type.
We show that Whitney?s approximation theorem holds in a general setting including spaces of (ultra)differentiable functions and ultradistributions. This is used to obtain real analytic modifications for differentiable functions including optimal estimates. Finally, a surjectivity criterion for continuous linear operators between Fréchet sheaves is deduced, which can be applied to the boundary value problem for holomorphic functions and to convolution operators in spaces of ultradifferentiable functions...
A note on the Cauchy-Bochner formula for a class of Beurling ultradistributions
A note on the distributional boundary values of analytic functions
A Phragmén-Lindelöf type quasi-analyticity principle
Quasi-analyticity theorems of Phragmén-Lindelöf type for holomorphic functions of exponential type on a half plane are stated and proved. Spaces of Laplace distributions (ultradistributions) on ℝ are studied and their boundary value representation is given. A generalization of the Painlevé theorem is proved.
Analytic implementation of the duals of some spaces of infinitely differentiable functions.
Approximation of some regular distribution in by finite, convex, linear combinations of Blaschke distributions
Beurling-Gevrey tempered ultradistributions as boundary values
Boundary value representation for a class of Beurling ultradistributions
Boundary values of ultra-distributions of exponential type
Convolution equations in the space of Laplace distributions
A formal solution of a nonlinear equation P(D)u = g(u) in 2 variables is constructed using the Laplace transformation and a convolution equation. We assume some conditions on the characteristic set Char P.
Darstellung temperierter vektorwertiger Distributionen durch holomorphe Funktionen II.
Darstellung temperierter vektorwertiger Distributionen durch holomorphe Funktionen I.
Darstellung von Distributionen endlicher Ordnung als Randwerte zu hypoelliptischen Differentialoperatoren.
Décomposition microlocale analytique des distributions
Décomposition microlocale analytique des distributions
Nous dirons qu’un faisceau de groupes abéliens sur un espace topologique est souple si, étant un ouvert de , et des fermés de , toute section de sur à support dans est somme de sections à support dans et . Soit une variété analytique réelle, son fibré cotangent en sphères, le faisceau sur des microfonctions qui proviennent localement sur , de distributions. Nous montrons que le faisceau est souple. En particulier le faisceau sur , quotient des distributions par...
Distributional boundary values and the tempered ultra-distributions
Distributional boundary values in
Distributional boundary values in . II
Distributional boundary values in (IV)