Bochner's tube theorem

In mathematics, Bochner's tube theorem (named for Salomon Bochner) shows that every function holomorphic on a tube domain in

can be extended to the convex hull of this domain.

be a connected open set.

holomorphic on the tube domain

can be extended to a function holomorphic on the convex hull

A classic reference is [1] (Theorem 9).

The generalized version of this theorem was first proved by Kazlow (1979),[4] also proved by Boivin and Dwilewicz (1998)[5] under more less complicated hypothese.

be a connected submanifold of

Then every continuous CR function on the tube domain

can be continuously extended to a CR function on

By "Int ch(S)" we will mean the interior taken in the smallest dimensional space which contains "ch(S)".