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

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

2011-06-14

arxiv.org/abs/1106.2795v1

Mathematics

Complex Variables

Scientific paper

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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