A sequential theory of some spaces of generalized functions.
A sheaf of Boehmians
We show that Boehmians defined over open sets of ℝⁿ constitute a sheaf. In particular, it is shown that such Boehmians satisfy the gluing property of sheaves over topological spaces.
A Singular Convolution Equation In The Space Of Distributions
A Singular Convolution Equation In The Space Of Distributions II
A singular convolution equation in the space of distributions.
A singular convolution equation in the space of distribution. II.
A solution of the Cauchy problem in the class of absolutely continuous distribution-valued functions.
A space of generalized distributions
In this paper we use a duality method to introduce a new space of generalized distributions. This method is exactly the same introduced by Schwartz for the distribution theory. Our space of generalized distributions contains all the Schwartz distributions and all the multipole series of physicists and is, in a certain sense, the smallest space containing all these series.
A spectral analysis of automorphic distributions and Poisson summation formulas
Automorphic distributions are distributions on , invariant under the linear action of the group . Combs are characterized by the additional requirement of being measures supported in : their decomposition into homogeneous components involves the family , of Eisenstein distributions, and the coefficients of the decomposition are given as Dirichlet series . Functional equations of the usual (Hecke) kind relative to turn out to be equivalent to the invariance of the comb under some modification...
A splitting theory for the space of distributions
The splitting problem is studied for short exact sequences consisting of countable projective limits of DFN-spaces (*) 0 → F → X → G → 0, where F or G are isomorphic to the space of distributions D'. It is proved that every sequence (*) splits for F ≃ D' iff G is a subspace of D' and that, for ultrabornological F, every sequence (*) splits for G ≃ D' iff F is a quotient of D'
A structural theorem for distributions having S-asymptotic.
A system of partial differential equations with fractional derivatives.
A Tauberian theorem for distributions
The well-known general Tauberian theorem of N. Wiener is formulated and proved for distributions in the place of functions and its Ganelius' formulation is corrected. Some changes of assumptions of this theorem are discussed, too.
A theorem on kernel in the theory of operator-valued distributions
A uniqueness theorem for Boehmians of analytic type.
Abelian theorem for the Stieltjes transform of distributions.
Abelian Theorems for Distributional H-Transform.
Abelian theorems for transformable Boehmians.
Abelian theorems for Whittaker transforms.
About a family of distributional products important in the applications