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

ponderation functions used in this article are : $φ(γ)=(|γ|+n-1)!(-1)^{|γ|}, and so on . The fact that these ponderation functions increase exponentially makes most of formulas for the symbolic calculus of Bessel integral operators unavailable and then all results related to these ponderations functions in this paper are wrong