A Remark on Extensions of CR Functions from Hyperplanes

http://dx.doi.org/10.4153/CMB-2008-003-8
Canad. Math. Bull. 51(2008), 21-25

  Published:2008-03-01
 Printed: Mar 2008

In the characterization of the range of the Radon transform, one encounters the problem of the holomorphic extension of functions defined on $\R^2\setminus\Delta_\R$ (where $\Delta_\R$ is the diagonal in $\R^2$) and which extend as ``separately holomorphic" functions of their two arguments. In particular, these functions extend in fact to $\C^2\setminus \Delta_\C$ where $\Delta_\C$ is the complexification of $\Delta_\R$. 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 a more general statement. In this new setting it becomes a variant of the celebrated ``edge of the wedge" theorem of Ajrapetyan and Henkin.