Generalization of the Dunkl operator on the space of entire functions

A differential-difference operator on the space of all entire functions with the uniform convergence topology on compacts that is a natural generalization of the one dimensional Dunkl operator has been introduced. Dunkl operators play an important role in various fields of mathematics and physics. It was proved that any nontrivial generalized convolution operator generated by differential-difference operator is hypercyclic on space of all entire functions with the uniform convergence topology on compacts. A new class of hypercyclic operators on space of all entire functions that includes previously known classes was also constructed.