Boundary values of cohomology classes as hyperfunctions.(English)Zbl 0847.32007

The authors consider hyperfunctions on a totally real submanifold $$X$$ in $$\mathbb{C}^m$$. They define the boundary value of a holomorphic-function coefficient cohomology class of degree $$q(0 \leq q \leq m - 1)$$ in a wedge contained in $$\mathbb{C}^m$$ whose edge lies on an arbitrary $$m$$-dimensional totally real submanifold $$X$$. It is a hyperfunction on $$X$$ and equivalent to use the Dolbeault or the Čech realization of the cohomology. If the directed cone of the wedge is convex, the boundary value map is injective. The corresponding spaces of germs of hyperfunctions are characterized by their hypo-analytic wave front set.
Reviewer: M.Muro (Yanagido)

MSC:

 32A45 Hyperfunctions 32A40 Boundary behavior of holomorphic functions of several complex variables 46F15 Hyperfunctions, analytic functionals
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