## 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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### References:

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