logarithmically convex set

Suppose $G\subset{\mathbb{C}}^{n}$ , then we define

\log\lVert G\rVert:=\{(\log\lvert z_{1}\rvert,\ldots,\log\lvert z_{n}\rvert)% \in{\mathbb{R}}^{n}\mid(z_{1},\ldots,z_{n})\in G\}.

Definition.

We say $G\subset{\mathbb{C}}^{n}$ is a logarithmically convex set if $\log\lVert G\rVert\subset{\mathbb{R}}^{n}$ is a convex set.

References

1 Steven G. Krantz. , AMS Chelsea Publishing, Providence, Rhode Island, 1992.

Title	logarithmically convex set
Canonical name	LogarithmicallyConvexSet
Date of creation	2013-03-22 14:29:32
Last modified on	2013-03-22 14:29:32
Owner	jirka (4157)
Last modified by	jirka (4157)
Numerical id	5
Author	jirka (4157)
Entry type	Definition
Classification	msc 32A07