A remark on extensions of CR functions from hyperplanes.

In the characterization of the range of the Radon transform, one encounters the problem of the holomorphic extension of functions defined on R2 \ R (where R is the diagonal in R2) and which extend as “separately holomorphic” functions of their two arguments. In particular, these functions extend in fact to C2 \ C where C is the complexification of R. We take this theorem from the integral geometry and put it in the more natural context of the CR geometry where it accepts an easier proof and amore general statement. In this new setting it becomes a variant of the celebrated “edge of the wedge” theorem of Ajrapetyan and Henkin