Abstract
In this paper, we study an approach of functional calculus in several variables developed for a particular case of commuting operators. This approach, which differs from the classical one, originates in the works of Fan-tappie. It is useful to obtain explicit solution to partial differential equations and holomorphic Cauchy problems, as well as to make a link between the holomorphic functional calculus, the theory of analytic functionals, and the Fantappie transform of analytic functionals.
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