117 citations · 882 across the 65 of their papers we have counts for
29 papers · 1 filter
On the completeness of the space
Michael Kunzinger, Norbert Ortner
We give a new proof of the completeness of the space by applying a criterion of compact regularity for the isomorphic sequence space $\lim_{k\rightarrow} (s\hat \ot…
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…
Inverse Function Theorems for Generalized Smooth Functions
Paolo Giordano, Michael Kunzinger
Generalized smooth functions are a possible formalization of the original historical approach followed by Cauchy, Poisson, Kirchhoff, Helmholtz, Kelvin, Heaviside, and Dirac to dea…
A convenient notion of compact set for generalized functions
Paolo Giordano, Michael Kunzinger
We introduce the notion of functionally compact sets into the theory of nonlinear generalized functions in the sense of Colombeau. The motivation behind our construction is to tran…
Strongly internal sets and generalized smooth functions
Paolo Giordano, Michael Kunzinger, Hans Vernaeve
Based on a refinement of the notion of internal sets in Colombeau's theory, so-called strongly internal sets, we introduce the space of generalized smooth functions, a maximal exte…
New topologies on Colombeau generalized numbers and the Fermat-Reyes theorem
Paolo Giordano, Michael Kunzinger
Based on the theory of Fermat reals we introduce new topologies on spaces of Colombeau generalized points and derive some of their fundamental properties. In particular, we obtain…