4 papers
Weak, strong and mixed extensions of relations to spaces of ultrafilters
Leonardo Raffaello Maximilian Gasparro, Lorenzo Luperi Baglini
The use of nonstandard methods to characterize properties of weak, strong and mixed extensions of congruences to ultrafilters has been the main topic of several recent papers. We s…
Rado equations solved by linear combinations of idempotent ultrafilters
Lorenzo Luperi Baglini, Paulo Henrique Arruda
We fully characterise the solvability of Rado equations inside linear combinations $a_{1}\U\oplus\dots\oplus a_{n}\U$ of idempotent ultrafilters $\U\inβ\Z$ by exploiting known rela…
Generalized solutions of variational problems and applications
Vieri Benci, Lorenzo Luperi Baglini, Marco Squassina
Ultrafunctions are a particular class of generalized functions defined on a hyperreal field that allow to solve variational problems with no class…
The category of Colombeau algebras
Lorenzo Luperi Baglini, Paolo Giordano
In [11], we introduced the notion of asymptotic gauge (AG), and we used it to construct Colombeau AG-algebras. This construction concurrently generalizes that of many different alg…