Monomial Expansions in Infinite Dimensional Holomorphy

Abstract

Let E and F denote locally convex spaces over C and let U denote an open subset of E. A function f: U→F is called holomorphic if

• a it is continuous,

• b. for each a ∈ U, υ ∈ E and $\phi \in F'$ the mapping $\lambda \in \mathbb{C} \to \phi o f(a + \lambda v)$ is holomorphic as a function of one complex variable on its domain of definition.