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Holomorphic extension and decomposition from a totally real manifold. (English) Zbl 0784.32004

The purpose of this paper is to develop hyperfunction theory on the totally real submanifold \(M\) in the complex vector space \(\mathbb{C}^ m\) from a point of view of boundary values of holomorphic functions. The author gives some method to decompose a hyperfunction on \(M\) into the boundary values. Then he deals with analytic wave front set of the hyperfunction, proves flabbiness of the sheaf of hyperfunctions on \(M\), relation between distribution boundary values and hyperfunction boundary values, and a \(\overline\partial\)-problem with partial compact support in some cylindrical domains. In particular, he provides a Greiner-Kohn-Stein condition for such a problem.
Reviewer: M.Muro (Yanagido)

MSC:

32A45 Hyperfunctions
32V40 Real submanifolds in complex manifolds
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