A theorem on kernel in the theory of operator-valued distributions
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.
Algebraic foundation of some distribution algebras
Algèbres différentielles et problème de Goursat non linéaire à données irrégulières
An Almost Orthogonal Radial Wavelet Expansion for Radial Distributions.
An embedding of Schwartz distributions in the algebra of asymptotic functions.
An extension of Duhamel's integral to differential equations involving generalized functions; the steady-state solution
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.
Analytic Regularizations, Finite Part Prescriptions and Products of Distributions.
Analytische Vektoren von Faltungshalbgruppen. I.
Another proof of the differentiability of a matrix
Applications of the smooth integral in the theory of weak solutions of ordinary differential equations
Approximations de type Hedberg dans les espaces et applications
Arbitrary complex powers of the Dirac operator on the hyperbolic unit ball.
Asymptotic Expansions of Schwartz's Distributions
Balanced Colombeau products of the distributions and
Results on singular products of the distributions and for natural are derived, when the products are balanced so that their sum exists in the distribution space. These results follow the pattern of a known distributional product published by Jan Mikusiński in 1966. The results are obtained in the Colombeau algebra of generalized functions, which is the most relevant algebraic construction for tackling nonlinear problems of Schwartz distributions.
Beitrag zum Divisionsproblem für Ultradistributionen und ein Fortsetzungsansatz.
Boehmians of type S and their Fourier transforms
Function spaces of type S are introduced and investigated in the literature. They are also applied to study the Cauchy problem. In this paper we shall extend the concept of these spaces to the context of Boehmian spaces and study the Fourier transform theory on these spaces. These spaces enable us to combine the theory of Fourier transform on these function spaces as well as their dual spaces.