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 .
|||V.S. Vladimirov, "Methods of the theory of functions of several complex variables" , M.I.T. (1966) (Translated from Russian)|
|||S. Bochner, W.T. Martin, "Several complex variables" , Princeton Univ. Press (1948)|
|[a1]||H. Behnke, P. Thullen, "Theorie der Funktionen meherer komplexer Veränderlichen" , Springer (1970) (Elraged & Revised Edition. Original: 1934)|
Hartogs domain. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Hartogs_domain&oldid=15532