Inversion formulas for complex radon transform on projective varieties and boundary value problems for systems of linear PDEs

Abstract

Let G ⊂ ℂPn be a linearly convex compact set with smooth boundary, D = ℂPn \ G, and let D* ⊂ (ℂPn)* 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 RV: Hd,d−1(V ∩ D) → H1,0(D*) and explicit formulas for solutions of an appropriate boundary value problem for the corresponding system of differential equations with constant coefficients on D*.