Theory of Infraexponential Holomorphic Functions

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In this paper, we define the notion of O^^～-pseudoconvex open sets without using the technical conditions of Kawai[13], [14]. Thereby C^^<～n> can be considered as an O^^～-pseudoconvex open set. Further it is proved that an O^^～-pseudoconvex open set is an open set in C^^<～n> whose finite part is pseudoconvex open set in C^n. We prove that a domain of O^^～-holomorphy is an O^^～-pseudoconvex open set. But the converse is an open problem.

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