Recent developments on the Stieltjes transform of generalized functions.
Over the past few years there has been considerable progress in the structural understanding of special Colombeau algebras. We present some of the main trends in this development: non-smooth differential geometry, locally convex theory of modules over the ring of generalized numbers, and algebraic aspects of Colombeau theory. Some open problems are given and directions of further research are outlined.
nbspAbstract. We give the definition of regular distributions and some characterizations of absolutely regular and regular -distributions.
In this paper first order linear ordinary differential equations are considered. It is shown that the Cauchy problem for these systems has a unique solution in , where denotes the Colombeau algebra.
In this paper we consider some spaces of differentiable multifunctions, in particular the generalized Orlicz-Sobolev spaces of multifunctions, we study completeness of them, and give some theorems.