A Remark on Extensions of CR Functions from Hyperplanes

Baracco, Luca

Canadian mathematical bulletin, Tome 51 (2008) no. 1, pp. 21-25

Résumé

In the characterization of the range of the Radon transform, one encounters the problem of the holomorphic extension of functions defined on ${{\mathbb{R}}^{2}}\backslash \,{{\Delta }_{\mathbb{R}}}$ (where ${{\Delta }_{\mathbb{R}}}$ is the diagonal in ${{\mathbb{R}}^{2}}$ ) and which extend as “separately holomorphic” functions of their two arguments. In particular, these functions extend in fact to ${{\mathbb{C}}^{2}}\,\backslash \,{{\Delta }_{\mathbb{C}}}$ where ${{\Delta }_{\mathbb{C}}}$ is the complexification of ${{\Delta }_{\mathbb{R}}}$ . We take this theorem from the integral geometry and put it in the more natural context of the $\text{CR}$ 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.

Détail

DOI : 10.4153/CMB-2008-003-8

Mots-clés : 32D10, 32V25