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Inversion formulas for complex radon transform on projective varieties and boundary value problems for systems of linear PDEs |
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| Authors: | Gennadi M Henkin Peter L Polyakov |
| Institution: | 1. Institut de Mathématiques, Université Pierre et Marie Curie, Case 247, 4 place Jussieu, 75252, Paris, France 2. Central Economics and Mathematics Institute, Russian Academy of Sciences, Nakhimovskii pr. 47, Moscow, 117418, Russia 3. Department of Mathematics, University of Wyoming, Laramie, WY, 82071, USA |
| Abstract: | Let G ? ?P n be a linearly convex compact set with smooth boundary, D = ?P n \ G, and let D* ? (?P n )* be the dual domain. Then for an algebraic, not necessarily reduced, complete intersection subvariety V of dimension d we construct an explicit inversion formula for the complex Radon transform R V : H d,d?1(V ∩ D) → H 1,0(D*) and explicit formulas for solutions of an appropriate boundary value problem for the corresponding system of differential equations with constant coefficients on D*. |
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