On the composition of integral operators acting in tempered Colombeau algebras

TL;DR

This paper demonstrates that the composition of generalized integral operators is well-defined within the framework of Colombeau algebras of tempered generalized functions, ensuring mathematical consistency.

Contribution

It establishes the well-defined nature of composing generalized integral operators in tempered Colombeau algebras, extending the algebraic framework.

Findings

Composition is well-defined in Colombeau algebras

Ensures mathematical consistency of operator composition

Extends the algebraic framework for generalized functions

Abstract

We show that the generalised composition of generalised integral operators is well defined on the space Colombeau algebras of tempered generalised functions.