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Disks extremal with respect to interpolation constants.

Nguyen Van Trao (2000)

Publicacions Matemàtiques

We define a function μ from the set of sequences in the unit ball to R*+ by taking the greatest lower bound of the reciprocal of the interpolating constant of the sequences of the disk which get mapped to the given sequence by a holomorphic mapping from the disk to the ball. Its properties are studied in the spirit of the work of Amar and Thomas.

Division et extension dans des classes de Carleman de fonctions holomorphes

Vincent Thilliez (1998)

Banach Center Publications

Let Ω be a bounded pseudoconvex domain in 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 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 Ω ¯ ). The essential...

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