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Cauchy-Fantappiè-Leray formulas with local sections and the inverse Fantappiè transform. (English) Zbl 0757.32008
The main result of the paper is the proof of the implication \((2)\Rightarrow(1)\) in the following theorem.
Let \(D\subset\mathbb{P}^ n\) be a linearly convex domain, \(n>1\). Then the following conditions are equivalent:
(1) the Fantappiè transform \(F:H_ 0'(D)\to H_ 0(D^*)\) is an isomorphism;
(2) the domain \(D\) is \(\mathbb{C}\)-convex.
(The proof of the implication \((1)\Rightarrow(2)\) was given by Znamenskij.) The main tools used by the author in the proof are
(a) a new version of the Cauchy-Fantappiè-Leray representation formula for local Cauchy-Leray sections,
(b) the Oka-Stolzenberg criterion for a domain of holomorphy to be a Runge domain (with the new proof based on (a)).

MSC:
32E30 Holomorphic, polynomial and rational approximation, and interpolation in several complex variables; Runge pairs
32E10 Stein spaces, Stein manifolds
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References:
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