Extending Holomorphic Functions from Subvarieties

  • Kenzō Adachi
Part of the International Society for Analysis, Applications and Computation book series (ISAA, volume 9)

Abstract

Let D be a pseudoconvex domain in ℂ n and V a subvariety of D. The purpose of this paper is to survey the extension problem of holomorphic functions from V to D in various function spaces. First, we study extension theorems in bounded strictly pseudoconvex domains. Next, we discuss extension theorems in bounded weakly pseudoconvex domains with support function and analytic polyhedra. The main tools to construct extension functions are integral formulas in subvarieties obtained by Hatziafratis[27] and Berndtsson[15]. Further, we state the L 2 extension theorem of Ohsawa-Takegoshi[36] in bounded pseudoconvex domains. Finally, we give some counterexamples for extension problems.

Keywords

Holomorphic Function Integral Formula Convex Domain Pseudoconvex Domain Stein Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Kenzō Adachi
    • 1
  1. 1.Department of Mathematics, Faculty of EducationNagasaki UniversityNagasakiJapan

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