Division et extension dans des classes de Carleman de fonctions holomorphes

Thilliez, Vincent

Banach Center Publications, Tome 43 (1998), p. 233-246 / Harvested from The Polish Digital Mathematics Library

Résumé

Let Ω be a bounded pseudoconvex domain in $ℂ^{n}$ with $C^{1}$ boundary and let X be a complete intersection submanifold of Ω, defined by holomorphic functions $v_{1}, . . ., v_{p}$ (1 ≤ p ≤ n-1) smooth up to ∂Ω. We give sufficient conditions ensuring that a function f holomorphic in X (resp. in Ω, vanishing on X), and smooth up to the boundary, extends to a function g holomorphic in Ω and belonging to a given strongly non-quasianalytic Carleman class $l! M_{l}$ in $\bar{Ω}$ (resp. satisfies $f = v_{1} f_{1} + . . . + v_{p} f_{p}$ with $f_{1}, . . ., f_{p}$ holomorphic in Ω and $l! M_{l}$ -regular in $\bar{Ω}$ ). The essential assumption is that f and $v_{1}, . . ., v_{p}$ belong to some (maybe smaller) Carleman class $l! M_{l}^{-}$ , where the sequences $M^{-}$ and M are precisely related by geometric conditions on X and Ω.

Publié le : 1998-01-01

Zbl 0942.32011

EUDML-ID : urn:eudml:doc:208887

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     author = {Thilliez, Vincent},
     title = {Division et extension dans des classes de Carleman de fonctions holomorphes},
     journal = {Banach Center Publications},
     volume = {43},
     year = {1998},
     pages = {233-246},
     zbl = {0942.32011},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv44i1p233bwm}
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Thilliez, Vincent. Division et extension dans des classes de Carleman de fonctions holomorphes. Banach Center Publications, Tome 43 (1998) pp. 233-246. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv44i1p233bwm/

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