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Ce travail est une étude analytique locale de l’anneau des séries de Dirichlet
convergentes. Dans un premier temps, on établit des propriétés arithmétiques de cet
anneau ; on prouve en particulier sa factorialité, que l’on déduit de théorèmes de
division du type Weierstrass. Ensuite, on s’intéresse à des problèmes de composition.
Soient et des séries de Dirichlet convergentes. On sait que
avec est encore une série de Dirichlet
convergente. On étudie la réciproque : sous les hypothèses que...
Let Ω be a bounded pseudoconvex domain in with boundary and let X be a complete intersection submanifold of Ω, defined by holomorphic functions (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 in (resp. satisfies with holomorphic in Ω and -regular in ). The essential...
We prove that any divisor of a global analytic set has a generic equation, that is, there is an analytic function vanishing on with multiplicity one along each irreducible component of . We also prove that there are functions with arbitrary multiplicities along . The main result states that if is pure dimensional, is locally principal, is not connected and represents the zero class in then the divisor is globally principal.
In this paper we study the degeneration of both the cohomology and the cohomotopy Frölicher spectral sequences in a special class of complex manifolds, namely the class of compact nilmanifolds endowed with a nilpotent complex structure. Whereas the cohomotopy spectral sequence is always degenerate for such a manifold, there exist many nilpotent complex structures on compact nilmanifolds for which the classical Frölicher spectral sequence does not collapse even at the second term.
On démontre que les domaines bornés, pseudo-convexes, à frontière lisse, de type fini dans , ayant un groupe d’automorphismes non compact sont biholomorphes à des domaines de la forme , où est un polynôme sousharmonique dont le degré est majoré par le type de la frontière du domaine.
In this note we establish a vector-valued version of Beurling’s theorem (the Lax-Halmos theorem) for the polydisc. As an application of the main result, we provide necessary and sufficient conditions for the “weak” completion problem in .
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