Hardy and Cowling-Price theorems for a~Cherednik type operator on the real line

Abstract

Hardy and Cowling-Price theorems for a Cherednik type operator on the real line Mohamed Ali MourouAbstract. This paper is aimed to establish Hardy and Cowling-Price type theorems for the Fourier transform tied to a generalized Cherednik operator on the real line.

Qualitative uncertainty principles for the generalized Fourier transform associated to a Dunkl type operator on the real line

“…We note that Mourou in [26] has studied only partial version of Hardy's and Cowling-Price's theorems to the Dunkl type operator on the real line and only for = 0. The method used is based on the relation between the generalized Fourier transform and the classical Fourier transform on R, and on the positivity of the transmutation operators relating to the Dunkl type operator on R. This method allows to give the analogue of the uncertainty principles within the framework of the generalized Fourier transform, contrary to the method of Mourou, which is based on the estimations of the eigenfunction of the operator , and the generalized heat kernel, which give only partial versions of Hardy's and Cowling-Price's theorem.…”

Miyachi's theorems associated with a differential- difference operator on the real line

“…and [1,4,5,8,12,10]). The purpose of this paper is a generalisation of Miyachi's theorem for F The structure of this paper is as follows.…”