Pompeiu-type theorem associated with the Dunkl operator on the real line.

In this work, by using the Wiener-Tauberian Theorem, we establish a Pompeiu-type theorem (which consists to study the uniqueness of some convolution equations solutions) associated with a differential-difference operator ?? a , called the Dunkl operator on the real line. Next, we give some applications. [ABSTRACT FROM AUTHOR]