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Article
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Transactions of the American Mathematical Society
Article . 1975 . Peer-reviewed
Data sources: Crossref
Transactions of the American Mathematical Society
Article . 1975 . Peer-reviewed
Data sources: Crossref
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Holomorphic functions on nuclear spaces

Authors: Philip J. Boland;

Holomorphic functions on nuclear spaces

Abstract

The space H ( E ) \mathcal {H}(E) of holomorphic functions on a quasi-complete nuclear space is investigated. If H ( E ) \mathcal {H}(E) is endowed with the compact open topology, it is shown that H ( E ) \mathcal {H}(E) is nuclear if and only if E ′ E’ (continuous dual of E E ) is nuclear. If E E is a D F N \mathcal {D}FN (dual of a Fréchet nuclear space) and F F is a closed subspace of E E , then the restriction mapping H ( E ) → H ( F ) \mathcal {H}(E) \to \mathcal {H}(F) is a surjective strict morphism.

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Keywords

Other ``topological'' linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than \(\mathbb{R}\), etc.), Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces), Topological linear spaces of continuous, differentiable or analytic functions, Other generalizations of function theory of one complex variable

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    citations
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    41
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Top 10%
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Top 10%
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
41
Average
Top 10%
Top 10%
bronze