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A remark on the theorem of Ohsawa-Takegoshi

Published online by Cambridge University Press:  22 January 2016

Klas Diederich  and
Emmanuel Mazzilli
Klas Diederich
Affiliation:
Mathematik, Unimersität Wuppertal, Gausstr. 20, D-42095 Wuppertal, Germany
Emmanuel Mazzilli
Affiliation:
UFR de Mathématiques Pures et Appliqués, Université de Lille, F-59655 Villeneuve d’Ascq Cedex, France
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If D ⊂ ℂn is a pseudoconvex domain and X ⊂ D a closed analytic subset, the famous theorem B of Cartan-Serre asserts, that the restriction operator r : (D) → (X) mapping each function F to its restriction F|X is surjective. A very important question of modern complex analysis is to ask what happens to this result if certain growth conditions for the holomorphic functions on D and on X are added.

Keywords

32A3632T9932T15
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 158 , December 2000 , pp. 185 - 189
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2000

References

[1] Diederich, K., and Mazzilli, E., Extension and restriction of holomorphic functions, Ann. Inst. Fourier, 47 (1997), 1079–1099.CrossRefGoogle Scholar
[2] Manivel, L., Un théorème de prolongement L 2 pour des sections holomorphes d’unfibré hermitien, Math. Z., 212 (1993), 107–122.CrossRefGoogle Scholar
[3] Ohsawa, T., and Takegoshi, K., On the extension of L 2-holomorphic functions, Math. Z., 195 (1987), 197–204.CrossRefGoogle Scholar