Representation Theorems for Tempered Ultradistributions
Right inverses for partial differential operators on Fourier hyperfunctions
We characterize the partial differential operators P(D) admitting a continuous linear right inverse in the space of Fourier hyperfunctions by means of a dual (Ω̅)-type estimate valid for the bounded holomorphic functions on the characteristic variety near . The estimate can be transferred to plurisubharmonic functions and is equivalent to a uniform (local) Phragmén-Lindelöf-type condition.
Singularités non dégénérées des systèmes de Gauss-Manin réticulés
Solutions hyperfonctions du problème de Cauchy
Some topological properties of the algebra of generalized hyperfunctions on the circle.
Spaces of analytic functions
Stability of a quadratic functional equation in the spaces of generalized functions.
Stability of cubic functional equation in the spaces of generalized functions.
Stability of quartic functional equations in the spaces of generalized functions.
Stability of trigonometric functional equations in generalized functions.
Strong boundary values : independence of the defining function and spaces of test functions
The notion of “strong boundary values” was introduced by the authors in the local theory of hyperfunction boundary values (boundary values of functions with unrestricted growth, not necessarily solutions of a PDE). In this paper two points are clarified, at least in the global setting (compact boundaries): independence with respect to the defining function that defines the boundary, and the spaces of test functions to be used. The proofs rely crucially on simple results in spectral asymptotics.
Supports des fonctionnelles analytiques
Supports des profonctionnelles analytiques
Syzygies of modules and applications to propagation of regularity phenomena.
Propagation of regularity is considered for solutions of rectangular systems of infinite order partial differential equations (resp. convolution equations) in spaces of hyperfunctions (resp. C∞ functions and distributions). Known resulys of this kind are recovered as particular cases, when finite order partial differential equations are considered.
The existence and the continuation of holomorphic solutions for convolution equations in tube domains
The Mellin analytic functionals and the Laplace—Beltrami operator on the Minkowski half-plane
The micro-support of the complex defined by a convolution operator in tube domains
The stationary phase method in Gevrey classes and Fourier integral operators on ultradistributions
The Taylor transformation of analytic functionals with non-bounded carrier
Let L be a closed convex subset of some proper cone in ℂ. The image of the space of analytic functionals Q'(L) with non-bounded carrier in L under the Taylor transformation as well as the representation of analytic functionals from Q'(L) as the boundary values of holomorphic functions outside L are given. Multipliers and operators in Q'(L) are described.
The ultra-distributions of exponential type of J. Sebastião e Silva