An Edge-of-the Wedge Theorem for Hypersurface CR Functions

Abstract

The Lewy extension theorem asserts the holomorphic extendability of CR functions defined in a neighborhood of a point on a hypersurface in C^{n+1}. The edge-of-the-wedge theorem asserts the extendability of holomorphic functions defined in wedges in C^{n+1} with edge a maximally real submanifold. In this article we prove under suitable hypotheses the holomorphic extendability to an open set in C^{n+1} of CR functions defined in the intersection of a hypersurface with a wedge whose edge is contained in the hypersurface. Unlike the situation for the classical edge-of-the-wedge theorem, for this hypersurface version extendability generally depends on the direction of the wedge.

17 pages, 1 figure. This revised version remarks on how our results compare with an extension theorem of Tumanov