Complex integral geometry and Penrose's representation of~the solutions of~Maxwell's equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 43 (1980) no. 1, pp. 18-31

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Penrose transformation is presented in terms of integral geometry. The kernel of the transformation is characterized and inverse operator is constructed, in an explicit way.
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S. G. Gindikin; G. M. Henkin. Complex integral geometry and Penrose's representation of~the solutions of~Maxwell's equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 43 (1980) no. 1, pp. 18-31. http://geodesic.mathdoc.fr/item/TMF_1980_43_1_a1/