This paper is devoted to the development and analysis of the linear canonical Opdam-Cherednik wavelet transform. We first introduce a generalized translation operator and a corresponding convolution product associated with the linear canonical Opdam-Cherednik transform, and we examine their fundamental properties. Building on this framework, we define the linear canonical Opdam-Cherednik wavelet transform, investigate its main characteristics. Finally, we derive an explicit inversion formula and we establish a Parseval-type identity for the continuous Linear canonical Opdam-Cherednik wavelet transform.
Abdallah, Nabiha, Ben (Fri,) studied this question.