Pommier Operator in Spaces of Analytic Functions of Several Complex Variables

Pommier operators in spaces of analytic functions of several complex variables are examined. Linear continuous operators that commute with the system of Pommier operators in the space $A(\Omega)$ of analytic functions in a polycylindrical domain $\Omega$ and in the countable inductive limit of Fréchet weighted spaces of entire functions are described. Cyclic vectors of the system of Pommier operators in the space $A(\Omega)$ are studied.