# Hartogs domain

From Encyclopedia of Mathematics

*semi-circular domain, with symmetry plane *

A domain in the space of complex variables which, for each point , contains the circle

Named after F. Hartogs. A Hartogs domain is called complete if for each point it contains the disc

A Hartogs domain with symmetry plane can conveniently be represented by a Hartogs diagram, viz., by the image of the Hartogs domain under the mapping .

#### References

[1] | V.S. Vladimirov, "Methods of the theory of functions of several complex variables" , M.I.T. (1966) (Translated from Russian) |

[2] | S. Bochner, W.T. Martin, "Several complex variables" , Princeton Univ. Press (1948) |

#### Comments

#### References

[a1] | H. Behnke, P. Thullen, "Theorie der Funktionen meherer komplexer Veränderlichen" , Springer (1970) (Elraged & Revised Edition. Original: 1934) |

**How to Cite This Entry:**

Hartogs domain.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Hartogs_domain&oldid=15532

This article was adapted from an original article by E.M. Chirka (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article