On the Hadamard multiplication theorem in ℂ n

Abstract

The Hadamard product of two holomorphic functions given by Taylor series ∑ α a α z α and ∑ α b α z α , defined on neighborhoods Ω 1 and Ω 2 of the origin, is the function whose Taylor series is ∑ α a α b α z α . For n = 1 , it is known that the Hadamard product extends to a holomorphic function on the so-called *-product of Ω 1 and Ω 2 . In this paper, we generalize this result to the case of several complex variables.