Normal families of holomorphic functions and mappings on a banach space
SCIE
- Title
- Normal families of holomorphic functions and mappings on a banach space
- Authors
- Kim, KT; Krantz, SG
- Date Issued
- 2003-01
- Publisher
- URBAN & FISCHER VERLAG
- 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 axe derived. Montel-type theorems axe 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 axe presented.
- Keywords
- holomorphic function; holomorphic mapping; Banach space; normal family; normal function; INFINITE-DIMENSIONAL HOLOMORPHY; LOCALLY CONVEX-SPACES; DOLBEAULT COMPLEX; APPROXIMATION; VARIABLES; DOMAINS
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/29706
- DOI
- 10.1016/S0723-0869(03)80001-4
- ISSN
- 0723-0869
- Article Type
- Article
- Citation
- EXPOSITIONES MATHEMATICAE, vol. 21, no. 3, page. 193 - 218, 2003-01
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