Isomorphy classes of spaces of holomorphic functions on open polydiscs in dual power series spaces
Studia Mathematica, Tome 101 (1991) no. 1, pp. 83-104
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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{10_4064_sm_101_1_83_104,
author = {Manfred Scheve},
title = {Isomorphy classes of spaces of holomorphic functions on open polydiscs in dual power series spaces},
journal = {Studia Mathematica},
pages = {83--104},
publisher = {mathdoc},
volume = {101},
number = {1},
year = {1991},
doi = {10.4064/sm-101-1-83-104},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-101-1-83-104/}
}
TY - JOUR AU - Manfred Scheve TI - Isomorphy classes of spaces of holomorphic functions on open polydiscs in dual power series spaces JO - Studia Mathematica PY - 1991 SP - 83 EP - 104 VL - 101 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/sm-101-1-83-104/ DO - 10.4064/sm-101-1-83-104 LA - en ID - 10_4064_sm_101_1_83_104 ER -
%0 Journal Article %A Manfred Scheve %T Isomorphy classes of spaces of holomorphic functions on open polydiscs in dual power series spaces %J Studia Mathematica %D 1991 %P 83-104 %V 101 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/sm-101-1-83-104/ %R 10.4064/sm-101-1-83-104 %G en %F 10_4064_sm_101_1_83_104
Manfred Scheve. Isomorphy classes of spaces of holomorphic functions on open polydiscs in dual power series spaces. Studia Mathematica, Tome 101 (1991) no. 1, pp. 83-104. doi: 10.4064/sm-101-1-83-104
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