The Exponential Representation of Holomorphic Functions of Uniformly Bounded Type

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 exponen...

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Bibliographic Details
Published in:	Journal of the Australian Mathematical Society (2001) Vol. 76; no. 2; pp. 235 - 246
Main Author:	Quang, Thai Thuan
Format:	Journal Article
Language:	English
Published:	Cambridge, UK Cambridge University Press 01.04.2004
Subjects:	32B10 46A63 46E50 Analytic functions Entire functions exponential representation holomorphic functions holomorphic functions of uniform bounded type primary 32A10 topological linear invariants exponential representation 32B10 holomorphic functions 46E50 46A63 primary 32A10 holomorphic functions of uniform bounded type topological linear invariants
ISSN:	1446-7887, 1446-8107
Online Access:	Get full text
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Summary:	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).
Bibliography:	PII:S1446788700008922 istex:54EFA371D06C04FD3CF4F5DD8C9FC48DE24137D7 ArticleID:00892 ark:/67375/6GQ-WL3GQ0HF-T ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1446-7887 1446-8107
DOI:	10.1017/S1446788700008922