The Rubin's q-wavelet packets

Using the q-harmonic analysis associated with the q-Rubin operator, we study three types of q-wavelet packets and their corresponding q-wavelet transforms. We give for these wavelet transforms the related Plancherel and inversion formulas as well as their q-scale discrete scaling functions

Sobolev type spaces associated with the q-Rubin's operator

In this paper we introduce and   study   some $q$-Sobolev type spaces by using the harmonic analysis associated with the q-Rubin operator. In particular, embedding theorems for these spaces are established.  Next, we introduce the q-Rubin potential spaces and study some of its properties

q-Analogue of the Dunkl Transform on the Real Line

[[abstract]]In this paper, we consider a q-analogue of the Dunkl operator on R, we dene and study its associated Fourier transform which is a q- analogue of the Dunkl transform. In addition to several properties, we establish an inversion formula and prove a Plancherel theorem for this q-Dunkl transform. Next, we study the q-Dunkl intertwining operator and its dual via the q-analogues of the Riemann-Liouville and Weyl transforms. Using this dual intertwining operator, we provide a relation between the q-Dunkl transform and the q2-analogue Fourier transform introduced and studied in [17, 18]

Wavelet Transform Associated with the q-Dunkl Operator

[[abstract]]In this paper, we present some new elements of harmonic analysis re- lated to the q-Dunkl operator introduced in [1], we dene and study the q-wavelets and the continuous q-wavelet transforms associated with this operator. Next, as an application, we give inversion formulas for the q-Dunkl intertwining operator and its dual using q-wavelets