Holomorphic functions with values in locally convex spaces and applications to integral formulas
Holomorphic functions with values in locally convex spaces and applications to integral formulas
复制标题
具有局部凸空间值的全纯函数及其在积分公式中的应用
DOI：
10.1090/s0002-9947-1964-0157004-9
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发表时间：
1964
影响因子：
1.3
通讯作者：
L. Bungart
中科院分区：
文献类型：
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作者：
L. Bungart
Grothendieck主要研究开函数空间的(拓扑)对偶空间的刻画。紧致的)黎曼球面的子集在局部凸空间中有值；随后的作者也是如此，他们把他的思想推广到黎曼曲面和多复变量的多圆域。我们的阐述目的是完全不同的。我们讨论了全纯函数的性质以及定义在解析空间上的取值于局部凸空间的全纯函数空间的性质。我们想把H.Cartan[5]的基本结果推广到这类更一般的函数，并给出一些应用。对于连续依赖于参数t E[0，1]的全纯函数族的非常特殊的情形，现有文献已经考虑并解决了其中的一些问题。这种全纯函数族可以被认为是取值于单位区间上连续函数的Banach空间%‘[0，1])的全纯函数
Grothendieck is mainly concerned with the characterisation of the (topological) dual space of the space of holomorphic functions on an open (resp. compact) subset of the Riemann sphere having values in a locally convex space; and so are subsequent authors who generalize his ideas to Riemann surfaces and multicircular domains in several complex variables. The purpose of our exposition is entirely different. We are concerned with properties of holomorphic functions and spaces of holomorphic functions with values in locally convex spaces which are defined on analytic spaces. We want to extend the basic results of H. Cartan [5] to this more general class of functions and give some applications. Some of these problems have already been considered and solved in the existing literature for the very special case of families of holomorphic functions depending continuously on a parameter t E [0,1]. Such families of holomorphic functions can be considered as holomorphic functions with values in the Banach space %'[0,1]) of continuous functions on the unit interval