Wavelet packets associated with singular partial-differential operators

Abstract

In this paper, we study some types of wavelet packets and the corresponding wavelet transforms associated with the Riemann Liouville operator on the half plane $[0,+\infty[\times\mathbb{R}$. For these transforms, we establish Plancherel theorems, orthogonality properties, Calderón’s reproducing formulas, reconstruction formulas and their scale discrete scaling functions.