q-ANALOGUE OF THE DUNKL TRANSFORM ON THE REAL LINE
نویسندگان
چکیده
In this paper, we consider a q-analogue of the Dunkl operator on R, we define 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 q-analogue Fourier transform introduced and studied in [17, 18].
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