Normal families of holomorphic functions on infinite dimensional spaces

Paula Takatsuka

Abstract: The purpose of the present work is to extend some classical results of holomorphic functions of one complex variable to holomorphic functions defined on infinite dimensional spaces. Montel-type and other classical theorems regarding normal families and exceptional values are established for holomorphic functions of infinitely many complex variables. This text culminates in a generalization of the classical Schottky Theorem, from which we derive Montel's fundamental criterion for normal families with exceptional values.

Keywords: holomorphic function; locally convex space; normal family; exceptional value.

Classification (MSC2000): 46G20, 46E50.

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