Modules Over the Ring of Ponderation functions with Applications to a Class of Integral Operators

TL;DR

This paper introduces modules over the ring of ponderation functions, linking harmonic analysis and ring theory, and demonstrates how integral transforms generate such modules.

Contribution

It presents a novel algebraic framework for harmonic analysis by defining modules over ponderation functions and explores their connection with classical integral transforms.

Findings

Laplace, Fourier, and Hankel transforms generate modules over ponderation functions.

Reinterprets harmonic analysis results through the lens of ring theory.

Establishes a new algebraic structure for integral operators.

Abstract

In this paper we introduce new modules over the ring of ponderation functions, so we recover old results in harmonic analysis from the side of ring theory. Moreover, we prove that Laplace transform, Fourier transform and Hankel transform generate some kind of modules over the ring of ponderation functions.