Resumen de Fourier transforms and the Funk-Hecke theorem in convex geometry

Paul Goodey, Vladyslav Yaskin, Maryna Yaskina

• We apply Fourier transforms to homogeneous extensions of functions on Sn-1. This results in complex integral operators. The real and imaginary parts of these operators provide a pairing of stereological data that leads to new results concerning the determination of convex bodies as well as new settings for known results. Applying the Funk�Hecke theorem to these operators yields stability versions of the results.