Nonlinear generalized sections and vector bundle homomorphisms in Colombeau spaces of generalized functions

TL;DR

This paper develops a framework for manifold-valued generalized functions and vector bundle homomorphisms within Colombeau algebras, providing new characterizations and extending the mathematical tools for nonlinear analysis in generalized function spaces.

Contribution

It introduces and characterizes spaces of manifold-valued generalized functions and vector bundle homomorphisms in Colombeau algebras, with point value characterizations.

Findings

Defined manifold-valued generalized functions in Colombeau spaces

Characterized vector bundle homomorphisms in this setting

Established point value characterizations for these spaces

Abstract

We define and characterize spaces of manifold-valued generalized functions and generalized vector bundle homomorphisms in the setting of the full diffeomorphism-invariant vector-valued Colombeau algebra. Furthermore, we establish point value characterizations for these spaces.