42 citations · 107 across the 22 of their papers we have counts for
27 papers
Generalized functions with infinitesimals
Hans Vernaeve
We give a survey of the use of infinitesimals within mathematical analysis to rigorously deal with the delta-function from physics, and more generally, with distributions in the se…
Topological Vector Spaces: a non-standard approach with monads and galaxies
Niels Charlier, Hans Vernaeve
A new and extensive formalism is developed for monads and galaxies in non-standard enlargements. It is shown that monads and galaxies can be manipulated using order-preserving and…
A Grothendieck topos of generalized functions I: basic theory
Paolo Giordano, Michael Kunzinger, Hans Vernaeve
The main aim of the present work is to arrive at a mathematical theory close to the historically original conception of generalized functions, i.e. set theoretical functions define…
Filter-dependent versions of the Uniform Boundedness Principle
Ben De Bondt, Hans Vernaeve
For every filter on , we introduce and study corresponding uniform -boundedness principles for locally convex topological vector spaces. These p…
A non-linear theory of infrahyperfunctions
Andreas Debrouwere, Hans Vernaeve, Jasson Vindas
We develop a nonlinear theory for infrahyperfunctions (also referred to as quasianalytic (ultra)distributions by L. Hörmander). In the hyperfunction case our work can be summarized…
Regularity of nonlinear generalized functions: a counterexample in the nonstandard setting
H. Vernaeve
Regularity theory in generalized function algebras of Colombeau type is largely based on the notion of -regularity, which reduces to -regularity when…