The Exponential Representation of Holomorphic Functions of Uniformly Bounded Type

Journal of the Australian Mathematical Society

Thai Thuan Quang¹ 

关键词: primary 32A10;    32B10;    46A63;    46E50;   

DOI  :  10.1017/S1446788700008922

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

It is shown that if E, F are Fréchet spaces, E ∈ (Hub), F ∈ (DN) then H(E, F) = Hub(E, F) holds. Using this result we prove that a Fréchet space E is nuclear and has the property (Hub) if and only if every entire function on E with values in a Fréchet space F ∈ (DN) can be represented in the exponential form. Moreover, it is also shown that if H(F*) has a LAERS and E ∈ (Hub) then H(E × F*) has a LAERS, where E, F are nuclear Fréchet spaces, F* has an absolute basis, and conversely, if H(E × F*) has a LAERS and F ∈ (DN) then E ∈ (Hub).

【 授权许可】

Unknown