摘要
设Ｘ，Ｙ是复数域Ｃ上的Ｈａｌｌｓｄｏｒｆｆ局部凸线性拓扑空间，ΩＣ．讨论了向量值全纯函数各种定义的等价性，主要结果有定理１设Ｘ是序列完备的，ｆ：Ω→Ｘ是弱全纯的，则ｆ：Ω→Ｘ＿β是强全纯的，从而ｆ：Ω→Ｘ是强全纯的．定理２ｆ：→Ｘ是强全纯的当且仅当它是局部全纯的。定理３设Ｘ是可数桶空间，则Ａ：Ω→Ｌ＿ｂ（Ｘ，Ｙ）是强全纯的当且仅当对每个ｘ∈Ｘ，映射λ→Ａ（λ）＿ｘ是强全纯的。推论１设Ｘ是可数桶空间，ｆ：Ω→·是弱全纯的，则ｆ：Ω→是强全纯的。
Let X and Y be Hausdorff locally convex linear topotogical spaces in complex field C and The equivalence of various definitions is studied for vector-valued holomorphic functions. The mainresults are :Theorem 1 Let X be sequentially complete and f: Ω→X weakly holomoaphic. Then f: Ω→X is strong holomorphic , so is f : Ω→X.Theorem. 2 f: Ω→X is strong holomorphic if and only if it is locally holomorphic.Theorem 3 Let X be numberably barrelled. Then A: Ω→L(X,Y)is strong holomorphic ifand only if the mapping λ→A(λ)x is strong holomorphic for all x ∈ X.Corollary 1 Let X be numberably barrelled and f: Ω→X weakly holomorphic. Then f:Ω→X_β is strong holomorphic.
出处
《西南师范大学学报（自然科学版）》
CAS
CSCD
1995年第2期111-115,共5页
Journal of Southwest China Normal University(Natural Science Edition)
关键词
拓扑空间
向量值
等价性
全纯函数
weakly holomorphic
strong holomorphic , locally holomorphlc
sequentially complete
numberably bairelled spaces
