Prolongement méromorphe de , et division des distributions, d’après I. N. Bernstein
Pseudodifferential operators with generalized symbols and regularity theory.
Quelques propriétés du noyau d'un opérateur différentiel linéaire non hypoelliptique, à coefficients constants
Regularization of distributions.
Regularization of Some Classes of Ultradistribution Semigroups and Sines
Regularized derivatives in a 2-dimensional model of self-interacting fields with singular data.
Regularly Varying Distributions
Regularly varying ultradistributions
Représentation discrète de fonctions généralisées
Representation of Distributions with Compact Support.
Representation Theorems for Tempered Ultradistributions
Results on Colombeau product of distributions
The differential -algebra of generalized functions of J.-F. Colombeau contains the space of Schwartz distributions as a -vector subspace and has a notion of ‘association’ that is a faithful generalization of the weak equality in . This is particularly useful for evaluation of certain products of distributions, as they are embedded in , in terms of distributions again. In this paper we propose some results of that kind for the products of the widely used distributions and , with in ,...
Results on generalized models and singular products of distributions in the Colombeau algebra
Models of singularities given by discontinuous functions or distributions by means of generalized functions of Colombeau have proved useful in many problems posed by physical phenomena. In this paper, we introduce in a systematic way generalized functions that model singularities given by distributions with singular point support. Furthermore, we evaluate various products of such generalized models when the results admit associated distributions. The obtained results follow the idea of a well-known...
Results on some neutrix convolutions of functions and distributions.
Results on the commutative neutrix convolution product of distributions
-linear algebra in economics and physics.
-linear operators in quantum mechanics and in economy.
Schwartz kernel theorem in algebras of generalized functions
A new approach to the generalization of Schwartz’s kernel theorem to Colombeau algebras of generalized functions is given. It is based on linear maps from algebras of classical functions to algebras of generalized ones. In particular, this approach enables one to give a meaning to certain hypotheses in preceding similar work on this theorem. Results based on the properties of -generalized functions class are given. A straightforward relationship between the classical and the generalized versions...
S'-convolvability with the Poisson kernel in the Euclidean case and the product domain case
We obtain real-variable and complex-variable formulas for the integral of an integrable distribution in the n-dimensional case. These formulas involve specific versions of the Cauchy kernel and the Poisson kernel, namely, the Euclidean version and the product domain version. We interpret the real-variable formulas as integrals of S’-convolutions. We characterize those tempered distribution that are S’-convolvable with the Poisson kernel in the Euclidean case and the product domain case. As an application...
Sequence space representations for zero-solutions of convolution equations on ultradifferentiable functions of Roumieu type