Normal families of holomorphic functions and mappings on a Banach space |
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Authors: | Kang-Tae Kim Steven G. Krantz |
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Affiliation: | 1Pohang University of Science and Technology, Pohang 790-784, Korea;2Department of Mathematics, Washington University, St. Louis, Missouri 63130, U.S.A. |
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Abstract: | The authors lay the foundations for the study of normal families of holomorphic functions and mappings on an infinite-dimensional normed linear space. Characterizations of normal families, in terms of value distribution, spherical derivatives, and other geometric properties are derived. Montel-type theorems are established. A number of different topologies on spaces of holomorphic mappings are considered. Theorems about normal families are formulated and proved in the language of these various topologies. Normal functions are also introduced. Characterizations in terms of automorphisms and also in terms of invariant derivatives are presented. |
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Keywords: | holomorphic function holomorphic mapping Banach space normal family normal function |
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