Let Λ_R(α) be a nuclear power series space of finite or infinite type with lim_{j→∞} (1/j) log α_j = 0. We consider open polydiscs D_a in Λ_R(α)'_b with finite radii and the spaces H(D_a) of all holomorphic functions on D_a under the compact-open topology. We characterize all isomorphy classes of the spaces {H(D_a) | a ∈ Λ_R(α), a > 0}. In the case of a nuclear power series space Λ₁(α) of finite type we give this characterization in terms of the invariants (Ω̅ ) and (Ω̃ ) known from the theory of linear operators between Fréchet spaces.
@article{bwmeta1.element.bwnjournal-article-smv101i1p83bwm,
author = {Manfred Scheve},
title = {Isomorphy classes of spaces of holomorphic functions on open polydiscs in dual power series spaces},
journal = {Studia Mathematica},
volume = {100},
year = {1991},
pages = {83-104},
zbl = {0812.46027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv101i1p83bwm}
}
Scheve, Manfred. Isomorphy classes of spaces of holomorphic functions on open polydiscs in dual power series spaces. Studia Mathematica, Tome 100 (1991) pp. 83-104. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv101i1p83bwm/
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