An application of internal objects to microlocal analysis in generalized function algebras

TL;DR

This paper demonstrates how internal objects can be utilized within Colombeau algebras to advance microlocal analysis in the nonlinear theory of generalized functions.

Contribution

It introduces a novel application of internal objects to microlocal analysis in Colombeau algebras, expanding the tools available for nonlinear generalized function theory.

Findings

Successful application of internal objects to microlocal analysis

Enhanced understanding of generalized function behavior

Potential for further research in nonlinear analysis

Abstract

We illustrate the use of internal objects in the nonlinear theory of generalized functions by means of an application to microlocal analysis in Colombeau algebras.