Fourier transform acting on the functions defined in the infinite LCA groups. A Grand Lebesgue Spaces approach

TL;DR

This paper derives exact norm estimates for the Fourier transform on functions in Grand Lebesgue Spaces over infinite local compact Abelian groups, providing precise bounds in this mathematical setting.

Contribution

It introduces a novel approach using Grand Lebesgue Spaces to obtain exact Fourier transform norms on infinite LCA groups, extending previous results.

Findings

Exact norm estimates for Fourier transform in GLS on infinite LCA groups

Extension of Fourier analysis techniques to Grand Lebesgue Spaces

Mathematical framework for analyzing Fourier transforms in this setting

Abstract

We derive in this article the exact norm in the Grand Lebesgue Spaces (GLS) estimates for Fourier transform acting on the functions defined in the infinite local compact Abelian (LCA) group, compact or discrete.