On a nonlinear Peetre's theorem in full Colombeau algebras

TL;DR

This paper extends Peetre's theorem to nonlinear local operators within the framework of full Colombeau algebras, providing insights into the structure of nonlinear generalized functions.

Contribution

It introduces a nonlinear version of Peetre's theorem tailored for full Colombeau algebras, advancing the understanding of local operators in this context.

Findings

Established a nonlinear Peetre's theorem for Colombeau algebras

Characterized representatives of nonlinear generalized functions

Enhanced the theoretical foundation of nonlinear generalized function analysis

Abstract

We adapt a nonlinear version of Peetre's theorem on local operators in order to investigate representatives of nonlinear generalized functions occurring in the theory of full Colombeau algebras.