Vector Fourier analysis on compact groups and Assiamoua spaces

TL;DR

This paper introduces Assiamoua spaces, a new family of function spaces, to extend Fourier analysis techniques to vector-valued functions on compact groups, enabling advanced analysis and Sobolev space construction.

Contribution

It defines Assiamoua spaces and demonstrates their fundamental role in vector-valued Fourier analysis on compact groups, bridging classic Fourier results with vector measure analysis.

Findings

Assiamoua spaces facilitate Fourier analysis of vector-valued functions.

The paper constructs Sobolev spaces of vector-valued functions on compact groups.

Classic Fourier analysis results are extended to vector-valued contexts.

Abstract

This paper shows how a family of function spaces (coined as Assiamoua spaces) plays a fundamental role in the Fourier analysis of vector-valued functions compact groups. These spaces make it possible to transcribe the classic results of Fourier analysis in the framework of analysis of vector-valued functions and vector measures. The construction of Sobolev spaces of vector-valued functions on compact groups rests heavily on the members of the aforementioned family.