On the valiron's theorem in the polydisk

In this paper, we discuss the Valiron's theorem in the unit polydisk DNDN. We prove that for a holomorphic map ϕ : DNDN → DNDN satisfying some regular conditions, there exists a holomorphic map θ : DNDN → H and a constant α >0 such that θ o ϕ =1αθ.It is based on the extension of Julia-Wolff-Carathéodory (JWC) theorem of DD in the polydisk.