  We use the remark that, through Bargmann-Fock representation, diagonal
operators of the Heisenberg-Weyl algebra are scalars for the Hadamard product
to give some properties (like the stability of periodic fonctions) of the
Hadamard product by a rational fraction. In particular, we provide through this
way explicit formulas for the multiplication table of the Hadamard product in
the algebra of rational functions in $\C[[z]]$.
