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Acta Mathematica Vietnamica

WEAK EXTENSION OF FRECHET-VALUED HOLOMORPHIC FUNCTIONS ON COMPACT SETS AND LINEAR TOPOLOGICAL INVARIANTS

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Abstract

It is shown that every holomorphic function on a nuclear Frechet space E with values in a Frechet space F is of uniform type if
E has the linear topological invariant (Ω~) and F has the linear topological invariant (DN) respectively. Based on the obtained result the equivalence of the holomorphicity and the weak holomorphicity of Frechet-valued functions on L~-regular compact subsets in a nuclear Frechet space is established.