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arXiv · 1106.2795

Inversion formulas for complex Radon transform on projective varieties and boundary value problems for systems of linear PDE

Gennadi M. Henkin·Peter L. Polyakov
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Abstract

Let $G\subset \C P^n$ be a linearly convex compact with smooth boundary, $D={\C}P^n\setminus G$, and let $D^* \subset (\C P^n)^*$ 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 $R_V:\ H^{d,d-1}(V\cap D)\to H^{1,0}(D^*)$, 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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Gennadi M. Henkin, Peter L. Polyakov. 2011-06-14. Inversion formulas for complex Radon transform on projective varieties and boundary value problems for systems of linear PDE. https://arxiv.org/abs/1106.2795

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