Geometrical embeddings for distributions into algebras of generalized functions

TL;DR

This paper introduces a spectral theory-based method to embed distributions into algebras of generalized functions on Riemannian manifolds, maintaining invariance under isometries and preserving singularities.

Contribution

It presents a novel spectral embedding technique that respects geometric invariances and the singularity structure of distributions.

Findings

Embeddings are invariant under isometries.

Singularity structures are preserved.

Method applies to closed Riemannian manifolds.

Abstract

We use spectral theory to produce embeddings of distributions in the algebras of generalized functions on a closed Riemannian manifold. These embeddings are invariant under isometries and preserve the singularity structure of the distributions.