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Siberian Mathematical Journal

, Volume 42, Issue 5, pp 952–960 | Cite as

One Boundary Version of Morera's Theorem

  • S. G. Myslivets
Article
  • 16 Downloads

Abstract

Let D be a bounded domain in Cn (n>1) with a connected smooth boundary ∂D and let f be a continuous function on ∂D. We consider conditions (generalizing those of the Hartogs–Bochner theorem) for holomorphic extendability of f to D. As a corollary we derive some boundary analog of Morera's theorem claiming that if the integrals of f vanish over the intersection of the boundary of the domain with complex curves in some class then f extends holomorphically to the domain.

Keywords

Continuous Function Bounded Domain Smooth Boundary Holomorphic Extendability Boundary Analog 
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

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • S. G. Myslivets
    • 1
  1. 1.Krasnoyarsk State UniversityKrasnoyarsk

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