Generalized functions as sequence spaces with ultranorms

TL;DR

This paper reviews a formulation of Colombeau algebras as sequence spaces with ultranorms, exploring extensions, generalizations, and applications in the context of generalized functions.

Contribution

It introduces a new perspective on Colombeau algebras as Hausdorff sequence spaces with ultranorms, extending previous results and exploring broader applications.

Findings

Extended the formulation of Colombeau algebras as sequence spaces with ultranorms.

Explored generalizations and new perspectives related to echelon spaces and asymptotic algebras.

Discussed applications and concepts of association in the context of generalized functions.

Abstract

We review our recent formulation of Colombeau type algebras as Hausdorff sequence spaces with ultranorms, defined by sequences of exponential weights. We extend previous results and give new perspectives related to echelon type spaces, possible generalisations, asymptotic algebras, concepts of association, and applications thereof.