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A Remark on Extensions of CR Functions from Hyperplanes

Published:2008-03-01
Printed: Mar 2008
• Luca Baracco
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Abstract

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.
 MSC Classifications: 32D10 - Envelopes of holomorphy 32V25 - Extension of functions and other analytic objects from CR manifolds

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