About a family of distributional products important in the applications
Acknowledgement of priority: Second derivates of convex functions.
Affine ultraregular generalized functions
Algebras of ultradifferentiable generalized functions satisfying some regularity assumptions are introduced. We give a microlocal analysis within these algebras related to the affine regularity type and the ultradifferentiability property. As a particular case we obtain new algebras of Gevrey generalized functions.
Algebra of multipliers on the space of real analytic functions of one variable
We consider the topological algebra of (Taylor) multipliers on spaces of real analytic functions of one variable, i.e., maps for which monomials are eigenvectors. We describe multiplicative functionals and algebra homomorphisms on that algebra as well as idempotents in it. We show that it is never a Q-algebra and never locally m-convex. In particular, we show that Taylor multiplier sequences cease to be so after most permutations.
Algebraic foundation of some distribution algebras
Algebraic quantum field theory and noncommutative moment problems. I
Algebraic quantum field theory and noncommutative moment problems. II
Algebras whose groups of units are Lie groups
Let A be a locally convex, unital topological algebra whose group of units is open and such that inversion is continuous. Then inversion is analytic, and thus is an analytic Lie group. We show that if A is sequentially complete (or, more generally, Mackey complete), then has a locally diffeomorphic exponential function and multiplication is given locally by the Baker-Campbell-Hausdorff series. In contrast, for suitable non-Mackey complete A, the unit group is an analytic Lie group without...
Algèbres différentielles et problème de Goursat non linéaire à données irrégulières
Almost periodic generalized solutions of differential equations
The paper aims to study systems of linear ordinary differential equations in the context of an algebra of almost periodic generalized ultradistributions. Conditions on the existence of generalized solutions are given.
An algebraic view of distributions and operators
An Almost Orthogonal Radial Wavelet Expansion for Radial Distributions.
An elementary theory of hyperfunctions and microfunctions
An embedding of Schwartz distributions in the algebra of asymptotic functions.
An equation in the left and right fractional derivatives of the same order
An extension of distributional wavelet transform
We construct a new Boehmian space containing the space 𝓢̃'(ℝⁿ×ℝ₊) and define the extended wavelet transform 𝓦 of a new Boehmian as a tempered Boehmian. In analogy to the distributional wavelet transform, it is proved that the extended wavelet transform is linear, one-to-one, and continuous with respect to δ-convergence as well as Δ-convergence.
An extension of Duhamel's integral to differential equations involving generalized functions; the steady-state solution
An intrinsic definition of the Colombeau generalized functions
A slight modification of the definition of the Colombeau generalized functions allows to have a canonical embedding of the space of the distributions into the space of the generalized functions on a manifold. The previous attempt in [5] is corrected, several equivalent definitions are presented.
An inversion formula and a note on the Riesz kernel
For potentials , where and are certain Schwartz distributions, an inversion formula for is derived. Convolutions and Fourier transforms of distributions in -spaces are used. It is shown that the equilibrium distribution with respect to the Riesz kernel of order , , of a compact subset of has the following property: its restriction to the interior of is an absolutely continuous measure with analytic density which is expressed by an explicit formula.
An Inversion Formula for the Distributional H-Transformation.