Quantum normal families: normal families of holomorphic functions and mappings on a Banach space

2002/12/03 by Kang-Tae Kim, Kang‐Tae Kim, Kim, Kang-Tae +3 · 1 citation
Mathematics · #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.CV #math.FA

paper · pdf · doi:10.48550/arxiv.math/0212034

35 pages

arxiv created 2002/12/03 · openalex publication_date 2002/12/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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