Abstract
The aim of this paper is to find some necessary and sufficient condi- tions by means of the property ( DN ) of E and the property ( LB ∞) of F under which Hw(X, F) = H (X, F) and Hδ(X, Hb(F ∗ )) = H (X, Hb(F ∗ )) where E, F are Frechet spaces and X is a compact determining polydisc in E ∗ . At the same time, we also study the problem of the local Dirichlet representation of separately holomorphic functions.
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