Bornologically isomorphic representations of distributions on manifolds

TL;DR

This paper demonstrates that the isomorphisms between distributional tensor fields and tensor fields with distributional coefficients also hold within the bornological framework, extending the mathematical understanding of these objects.

Contribution

It establishes bornologically isomorphic representations of distributional tensor fields, bridging the gap between classical and bornological approaches.

Findings

Isomorphisms hold in the bornological setting.

Extends classical tensor distribution theory.

Provides a new perspective on distributional tensor fields.

Abstract

Distributional tensor fields can be regarded as multilinear mappings with distributional values or as (classical) tensor fields with distributional coefficients. We show that the corresponding isomorphisms hold also in the bornological setting.