On Abel-Radon transform of locally residual currents

Details On Abel-Radon transform of locally residual currents On Abel-Radon transform of locally residual currents

2004-02-14

arxiv.org/abs/math/0402240v1

Mathematics

Complex Variables

26 pages

Scientific paper

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.

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