Christopher Boyd, Seán Dineen
Abstract
Abstract Compactness of locally bounded sets of holomorphic functions with infinite dimensional domains is connected, using Heinrich's density condition, to the Schwartz and semi‐Montel properties on the domain. The metrizability of bounded subsets for various spaces of holomorphic functions is investigated.
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Abstract Compactness of locally bounded sets of holomorphic functions with infinite dimensional domains is connected, using Heinrich's density condition, to the Schwartz and semi‐Montel properties on the domain. The metrizability of bounded subsets for various spaces of holomorphic functions is investigated.
Key concepts: Holomorphic function, Mathematics, Bounded function, Compact space, Identity theorem, Pure mathematics, Domain (mathematical analysis), Analyticity of holomorphic functions