Characterization of distributions having a value at a point in the sense of Robinson

We characterize Schwartz distributions having a value at a single point in the sense introduced by means of nonstandard analysis by A. Robinson. They appear to be distributions continuous in a neighborhood of the point.Comment: 5 page

Topological properties of regular generalized function algebras

We investigate density of various subalgebras of regular generalized functions in the special Colombeau algebra of generalized functions.Comment: 6 page

Classes of generalized functions with finite type regularities

We introduce and analyze spaces and algebras of generalized functions which correspond to Hölder, Zygmund, and Sobolev spaces of functions. The main scope of the paper is the characterization of the regularity of distributions that are embedded into the corresponding space or algebra of generalized functions with finite type regularities

An algebraic approach to manifold-valued generalized functions

We discuss the nature of structure-preserving maps of varies function algebras. In particular, we identify isomorphisms between special Colombeau algebras on manifolds with invertible manifold-valued generalized functions in the case of smooth parametrization. As a consequence, and to underline the consistency and validity of this approach, we see that this generalized version on algebra isomorphisms in turn implies the classical result on algebras of smooth functions.Comment: 7 page

On the Well-posedness of Some generalized Characteristic Cauchy Problems

By means of convenient regularization for an ill posed Cauchy problem, we define an associated generalized problem and discuss the conditions for the solvability of it. To illustrate this, starting from the semilinear unidirectional wave equation with data given on a characteristic curve, we show existence and uniqueness of the solution