7 papers
Bjork-DEbrowere algebras topologies and comparison of regularities
Anatole Khelif, Dimitris Scarpalezos
In this paper we investigate properties of the family of weight functions and especiallyin the "weight function" model. We etablish in theintroduced algebra topological sharp struc…
Topology and regularity for generalized ultradistribution algebras
Stevan Pilipovic, Dragana Risteski, Dimitris Scarpalezos +1
Compiling essential results for non-quasianalytic ultradistribution spaces and Colombeau versions of generalized ultradistribution algebras, we analyze strong - and strong -a…
Besov regularity in non-linear generalized functions
Stevan Pilipović, Dimitris Scarpalézos, Jasson Vindas
We introduce and study new modules and spaces of generalized functions that are related to the classical Besov spaces. Various Schwartz distribution spaces are naturally embedded i…
Local regularity in non-linear generalized functions
Stevan Pilipovic, Dimitris Scarpalezos, Jasson Vindas
In this review article we present regularity properties of generalized functions which are useful in the analysis of non-linear problems. It is shown that Schwartz distributions em…
Asymptotic ideals (ideals in the ring of Colombeau generalized constants with continuous parametrization)
Anatole Khelif, Dimitris Scarpalezos, Hans Vernaeve
We study the asymptotics at zero of continuous functions on (0, 1] by means of their asymptotic ideals, i.e., ideals in the ring of continuous functions on (0, 1] satisfying a poly…
Regularity properties of distributions through sequences of functions
Stevan Pilipovic, Dimitris Scarpalezos, Jasson Vindas
We give necessary and sufficient criteria for a distribution to be smooth or uniformly Hölder continuous in terms of approximation sequences by smooth functions; in particular, in…