On microfunctions at the boundary along CR manifolds |
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Authors: | Andrea d'Agnolo Giuseppe Zampieri |
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Affiliation: | (1) Mathématiques; Univ. Paris 6, 4, Place Jussieu, F-75252 Paris Cedex 05;(2) Dip. di Matematica, Università di Padova, via Belzoni 7, I-35131 Padova, Italy |
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Abstract: | Let X be a complex analytic manifold, a C2 submanifold, an openset with C2 boundary .Denote by (resp. ) the microlocalization along M (resp. ) of the sheaf of holomorphic functions.In the literature (cf. [A-G], [K-S 1,2])one encounters two classical results concerning the vanishing of the cohomology groups.The most general gives the vanishing outside a range of indices j whose length is equal to (with being the number of respectively positive, negative and null eigenvalues for themicrolocal Levi form ).The sharpest result gives the concentration in a single degree, provided that the difference is locally constant for near p (with for z the base point of p).The first result was restated for the complex in [D'A-Z 2], in the case codimWe extend it here to any codimension and moreover we also restate for the second vanishing theorem.We also point out that the principle of our proof, related to a criterion for constancy of sheaves due to [K-S 1], is a quite new one. |
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Keywords: | Solvability of the IE18" > /content/J325542QP34W26P7/10599_2004_Article_103468_TeX2GIFIE18.gif" alt="
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