On Abel-Radon transform of locally residual currents

Abstract

We give in this note a generalisation of the following theorem of Henkin and Passare : Let be Y an analytic subvariety of pure codimension p in a linearly p-concave domain U, and w a meromorphic q-form (q>0) on Y; if the Abel transform of w, which is meromorphic on U*, has a meromorphic prolongation to some greater domain U' * containing U^*, then Y extends as an analytic subvariety Y' of U', and w as a meromorphic form on Y'. We show the analogous statement when we replace the Abel transform of w by the Abel-Radon transform of a locally residual current on U.