Premium
Fourier transforms and the Funk–Hecke theorem in convex geometry
Author(s) -
Goodey Paul,
Yaskin Vladyslav,
Yaskina Maryna
Publication year - 2009
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdp035
Subject(s) - mathematics , homogeneous , regular polygon , fourier transform , operator theory , pure mathematics , funk , convex body , fourier analysis , mathematical analysis , geometry , convex optimization , combinatorics , physics , acoustics
We apply Fourier transforms to homogeneous extensions of functions on S n –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.