A new approach to diffeomorphism invariant algebras of generalized functions

TL;DR

This paper introduces a simplified and unified construction of diffeomorphism invariant Colombeau-type algebras of nonlinear generalized functions, making the framework more accessible for applications on manifolds.

Contribution

It provides a modern, compact, and unified formalism for constructing diffeomorphism invariant algebras of generalized functions, improving simplicity and accessibility.

Findings

Simplified construction of diffeomorphism invariant Colombeau algebras

Unified formalism applicable locally and on manifolds

Enhanced accessibility of the algebraic framework

Abstract

We develop the diffeomorphism invariant Colombeau-type algebra of nonlinear generalized functions in a modern and compact way. Using a unifying formalism for the local setting and on manifolds, the construction becomes simpler and more accessible than previously in the literature.