Manifold-valued generalized functions in full Colombeau spaces

TL;DR

This paper extends the theory of Colombeau algebras to include manifold-valued generalized functions, introducing new concepts like generalized vector bundle homomorphisms and tangent maps for advanced mathematical analysis.

Contribution

It introduces manifold-valued generalized functions within full Colombeau spaces and develops related concepts such as vector bundle homomorphisms and tangent maps.

Findings

Characterization results for manifold-valued generalized functions

Definition of generalized vector bundle homomorphisms

Introduction of tangent maps for these generalized functions

Abstract

We introduce the notion of generalized function taking values in a smooth manifold into the setting of full Colombeau algebras. After deriving a number of characterization results we also introduce a corresponding concept of generalized vector bundle homomorphisms and, based on this, provide a definition of tangent map for such generalized functions.