Mathematical Notes

, Volume 83, Issue 3, pp 500–505

On families of complex lines sufficient for holomorphic extension


DOI: 10.1134/S0001434608030231

Cite this article as:
Kytmanov, A.M. & Myslivets, S.G. Math Notes (2008) 83: 500. doi:10.1134/S0001434608030231


It is shown that the set \( \mathfrak{L}_\Gamma \) of all complex lines passing through a germ of a generating manifold Γ is sufficient for any continuous function f defined on the boundary of a bounded domain D ⊂ ℂn with connected smooth boundary and having the holomorphic one-dimensional extension property along all lines from \( \mathfrak{L}_\Gamma \) to admit a holomorphic extension to D as a function of many complex variables.

Key words

holomorphic extension property family of complex lines Hartogs’ theorem Bochner-Martinelli integral Sard’s theorem Cauchy-Riemann condition 

Copyright information

© Pleiades Publishing, Ltd. 2008

Authors and Affiliations

  1. 1.Krasnoyarsk State UniversityKrasnoyarskRussia

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