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Displaying similar documents to “Extension and restriction of holomorphic functions”

On D*-extension property of the Hartogs domains.

Do Duc Thai, Pascal J. Thomas (2001)

Publicacions Matemàtiques

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A complex analytic space is said to have the D*-extension property if and only if any holomorphic map from the punctured disk to the given space extends to a holomorphic map from the whole disk to the same space. A Hartogs domain H over the base X (a complex space) is a subset of X x C where all the fibers over X are disks centered at the origin, possibly of infinite radius. Denote by φ the function giving the logarithm of the reciprocal of the radius of the fibers, so that, when X is...

Zeros of bounded holomorphic functions in strictly pseudoconvex domains in ℂ 2

Jim Arlebrink (1993)

Annales de l'institut Fourier

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Let D be a bounded strictly pseudoconvex domain in ℂ 2 and let X be a positive divisor of D with finite area. We prove that there exists a bounded holomorphic function f such that X is the zero set of f . This result has previously been obtained by Berndtsson in the case where D is the unit ball in ℂ 2 .

Hartogs theorem for forms : solvability of Cauchy-Riemann operator at critical degree

Chin-Huei Chang, Hsuan-Pei Lee (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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The Hartogs Theorem for holomorphic functions is generalized in two settings: a CR version (Theorem 1.2) and a corresponding theorem based on it for C k ∂ ¯ -closed forms at the critical degree, 0 ≤ k ≤ ∞ (Theorem 1.1). Part of Frenkel’s lemma in C k category is also proved.