Fourier Analysis via Mild Distributions: Group Theoretical Aspects

TL;DR

This paper explores the use of mild distributions and Banach Gelfand Triples to advance Fourier analysis, emphasizing both theoretical foundations and practical applications.

Contribution

It introduces a framework connecting mild distributions with group theory to enhance Fourier analysis techniques.

Findings

Establishes a link between mild distributions and Fourier analysis

Provides a group-theoretical perspective on Fourier transforms

Lays groundwork for application-oriented Fourier analysis

Abstract

This note aims at providing a guide towards the use of mild distributions, or more generally the concept of Banach Gelfand Triples in the context of Fourier Analysis, both in the classical and the application oriented sense.