Fundamental Theorems of Fourier-Stieltjes Transform Defined by Induced Representation on Locally Compact Group

TL;DR

This paper extends the Fourier-Stieltjes transform for vector measures from compact groups to locally compact groups using induced group representations, broadening the transform's applicability.

Contribution

It introduces a method to define Fourier-Stieltjes transforms on locally compact groups via induced representations from compact subgroups, expanding the theoretical framework.

Findings

Extended Fourier-Stieltjes transform to locally compact groups

Established connection between induced representations and transforms

Provided mathematical foundation for future applications

Abstract

This work addresses an extension of Fourier-Stieltjes transform of a vector measure defined on compact groups to locally compact groups, by using a group representation induced by a representation of one of its compact subgroups.