Fourier transforms and the Funk-Hecke theorem in convex geometry
- Autores: Paul Goodey, Vladyslav Yaskin, Maryna Yaskina
- Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 80, Nº 2, 2009, págs. 388-404
- Idioma: inglés
- DOI: 10.1112/jlms/jdp035
- Enlaces
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Resumen
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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