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Microlocal pseudoconvexity and “edge of the wedge” theorem. (English) Zbl 0722.32012
At first, the authors prove that, for a bounded pseudoconvex domain $$\Omega$$ in $${\mathbb{C}}^ n$$ with real analytic boundary $$\partial \Omega$$ and an open subset $$\omega$$ of $$\partial \Omega$$, $$\Omega\cup \omega$$ has a fundamental system of pseudoconvex neighbourhoods. They consider a complex manifold X, its real analytic generic submanifold of codimension d, an open subset U of the conormal bundle $$T_ N*X$$, the Levi form of N having r negative eigenvalues, and the Sato’s microlocalization $$\mu_ N({\mathcal O}_ X)$$. They prove the flabbyness of the sheaf $$H^{d+r}(\mu_ N({\mathcal O}_ X))$$ under the assumption that U contains no germ of complex curve.

##### MSC:
 32T99 Pseudoconvex domains 32C35 Analytic sheaves and cohomology groups 58J15 Relations of PDEs on manifolds with hyperfunctions
##### Keywords:
Sato’s microlocalization
Full Text:
##### References:
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