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- W2129335315 abstract "Henkin et Passare ont démontré le théorème suivant : soit ω une q-forme méromorphe (q>0) sur un sous-ensemble analytique Y de codimension pure p d'un ouvert linéairement p-concave U⊂PN ; si la transformation d'Abel–Radon A(ω∧[Y]), qui est méromorphe sur U∗⊂G(p,N), se prolonge méromorphiquement dans un domaine U∗ contenant U∗, alors Y se prolonge en un sous-ensemble analytique Y du domaine U, et ω en une forme méromorphe sur Y. Le problème est de démontrer l'énoncé analogue, lorsqu'on remplace le courant ω∧[Y] par un courant α de bidegré (q+p,p), 0<q⩽N−p, de type plus général, appelé localement résiduel. Nous donnons la solution pour p=1, et q=N−p, ou q quelconque si A(α)=0. On donne pour terminer une application de ce théorème. Pour citer cet article : B. Fabre, C. R. Acad. Sci. Paris, Ser. I 338 (2004). The aim of this Note is to give a generalisation of the following theorem of Henkin and Passare: let Y be an analytic subvariety of pure codimension p in a linearly p-concave domain U, and ω a meromorphic q-form (q>0) on it; if the Abel–Radon transform A(ω∧[Y]), which is meromorphic on U∗, has a meromorphic prolongation to U∗, then Y extends to an analytic subvariety of U, and ω to a meromorphic form on it. The problem is to show the analogous statement when we replace ω∧[Y] by a current α of a more general type, called locally residual. We give the proof if α is of bidegree (N,1), or (q+1,1), 0<q<N in the particular case where A(α)=0. We conclude with some applications of the theorem. To cite this article: B. Fabre, C. R. Acad. Sci. Paris, Ser. I 338 (2004)." @default.
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- W2129335315 date "2004-05-01" @default.
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- W2129335315 title "Sur la transformation d'Abel–Radon de courants localement résiduels" @default.
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- W2129335315 doi "https://doi.org/10.1016/j.crma.2004.03.008" @default.
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