Geodesic
Contribution to the Hadamard multiplication theorem
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 75 (2021) no. 2, pp. 94-107.

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In this article we define a binary linear operator T for holomorphic functions in given open sets A and B in the complex plane under certain additional assumptions. It coincides with the classical Hadamard product of holomorphic functions in the case where A and B are the unit disk. We show that the operator T exists provided A and B are simply connected domains containing the origin. Moreover, T is determined explicitly by means of an integral form. To this aim we prove an alternative representation of the star product A*B of any sets A,B⊂ℂ containing the origin. We also touch the problem of holomorphic extensibility of Hadamard product.
Keywords: Hadamard product, holomorphic extension, star product, Hadamard multiplication theorem 
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Parol, Maciej; Partyka, Dariusz. Contribution to the Hadamard multiplication theorem. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 75 (2021) no. 2, pp. 94-107. http://geodesic.mathdoc.fr/item/AUM_2021_75_2_a5/

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