Mathematical Notes

, Volume 83, Issue 3, pp 500–505

On families of complex lines sufficient for holomorphic extension

Authors

    • Krasnoyarsk State University
  • S. G. Myslivets
    • Krasnoyarsk State University
Article

DOI: 10.1134/S0001434608030231

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

Abstract

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 propertyfamily of complex linesHartogs’ theoremBochner-Martinelli integralSard’s theoremCauchy-Riemann condition

Copyright information

© Pleiades Publishing, Ltd. 2008