Extension of CR-functions on wedges.

Abstract

The celebrated Boggess-Polking theorem [BP82] extending classical results of Lewy [L56] states that all (continuous) CR-functions on a generic submanifold M in CN extend holomorphically to a wedge in the direction of the convex cone spanned by the values of the (vector-valued) Levi form of M. Here one starts with a submanifold M and ends with a wedge. A natural question is to obtain a result generalizing the above one within the category of wedges with description of the additional directions of extendibility (see Tumanov [T95a, T95b] for general extension results to wedges without prescription of the direction)