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| Titel: |
Vanishing theorem for sheaves of microfunctions at the boundary on cr-manifolds |
| Auteur: |
D'Agnolo, Andrea Zampieri, Giuseppe |
| Verschenen in: |
Communications in partial differential equations |
| Paginering: | Jaargang 17 (1992) nr. 5-6 pagina's 989-999 |
| Jaar: |
1992 |
| Inhoud: |
Let X be a complex analytic manifold. Consider S⊂M⊂Xreal analytic submonifolds with codium RMS=1,and let ω be a connected component of M\S. Let p∈S XMTM*X where T*Xdenotes the conormal bundle to M in X, and denote by ν(p) the complex radial Euler field at p. Denote by μ*(Ox) (for * = M, ω) the microlocalization of the sheaf of holomorphic functions along *. Under the assumption dimR(TpTM*Xx∩ ν(p)) = 1, a theorem of vanishing for the cohomology groups HjμM(Ox)p is proved in [K-S 1, Prop. 11.3.1], j being related to the number of positive and negative eigenvalue for the Levi form of M. Under the hypothesis dimR(TpTS*X∩ν(p))=1, a similar result is proved here for the cohomology groups of the complex of microfunctions at the boundary μω(Ox).Stating this result in terms of regularity at the boundary for CR-hyperfunctions a local Bochner-type theorem is then obtained. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 135 van 135 gevonden artikelen
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