tube domain


Suppose Sn is an open set (usually connected), then we define


We call TS the tube domain associated to S.

Basically the idea is that these domains give you completePlanetmathPlanetmathPlanetmathPlanetmathPlanetmath freedom in the imaginary coordinates. An interesting fact about these domains is that TS is pseudoconvex if and only if TS is convex in the geometric sense, and this is true if and only if S itself is convex.


  • 1 Steven G. Krantz. , AMS Chelsea Publishing, Providence, Rhode Island, 1992.
Title tube domain
Canonical name TubeDomain
Date of creation 2013-03-22 14:32:44
Last modified on 2013-03-22 14:32:44
Owner jirka (4157)
Last modified by jirka (4157)
Numerical id 6
Author jirka (4157)
Entry type Definition
Classification msc 32A07