Fourier transforms and the Funk–Hecke theorem in convex geometry
نویسندگان
چکیده
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.
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