-Topologies on the Test Function Algebra
On a functional equation of Aczél and Chung.
On a limit at infinity notion of an ultradistribution. (Sur une notion de limite à l'infini d'une ultradistribution.)
On a nonlinear Peetre's theorem in full Colombeau algebras
We adapt a nonlinear version of Peetre's theorem on local operators in order to investigate representatives of nonlinear generalized functions occurring in the theory of full Colombeau algebras.
On a space of smooth functions on a convex unbounded set in ℝn admitting holomorphic extension in ℂn
For some given logarithmically convex sequence M of positive numbers we construct a subspace of the space of rapidly decreasing infinitely differentiable functions on an unbounded closed convex set in ℝn. Due to the conditions on M each function of this space admits a holomorphic extension in ℂn. In the current article, the space of holomorphic extensions is considered and Paley-Wiener type theorems are established. To prove these theorems, some auxiliary results on extensions of holomorphic functions...
On a testing-function space for distributions associated with the Kontorovich-Lebedev transform.
We construct a testing function space, which is equipped with the topology that is generated by Lν,p - multinorm of the differential operatorAx = x2 - x d/dx [x d/dx],and its k-th iterates Akx, where k = 0, 1, ... , and A0xφ = φ. Comparing with other testing-function spaces, we introduce in its dual the Kontorovich-Lebedev transformation for distributions with respect to a complex index. The existence, uniqueness, imbedding and inversion properties are investigated. As an application we find a solution...
On alternative functional equations. (Short Communication).
On an application of hypoellipticity to solutions of functional equations.
On Calderón's conjecture.
On complex interpolation with an analytic functional.
On convergence in some subspaces of generalized functions
On defining the generalized functions and .
On defining the product .
On distributions invariant with respect to some linear transformations
On distributions of rapid growth
On E. Borel's Theorem.
On extendability of invariant distributions
In this paper sufficient conditions are given in order that every distribution invariant under a Lie group extend from the set of orbits of maximal dimension to the whole of the space. It is shown that these conditions are satisfied for the n-point action of the pure Lorentz group and for a standard action of the Lorentz group of arbitrary signature.
On extension of Gabor transform to Boehmians
On formal trigonometrical series
On Fourier transforms of distributions with one-sided bounded carriers