The wavelet transform associated with the Jacobi–Cherednik operator

Abstract

In this paper, we introduce the wavelet transform associated with the Jacobi–Cherednik operator. We first present some basic properties of the Opdam–Cherednik wavelet transform. Then, we establish a few versions of the uncertainty principle for this transform. In particular, we study Donoho–Stark's uncertainty principle, Lieb's uncertainty principle, Benedicks-type uncertainty principle, and Heisenberg-type uncertainty principle for the Opdam–Cherednik wavelet transform. Finally, we obtain the Heisenberg-type uncertainty inequality using the k-entropy of this transform.