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Journal of the London Mathematical Society Advance Access originally published online on July 29, 2009
Journal of the London Mathematical Society 2009 80(2):388-404; doi:10.1112/jlms/jdp035
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© 2009 London Mathematical Society

Fourier transforms and the Funk–Hecke theorem in convex geometry

Paul Goodey

Department of Mathematics
University of Oklahoma
Norman, OK 73019
USA
pgoodey@math.ou.edu

Vladyslav Yaskin

Department of Mathematical and Statistical Sciences
University of Alberta
Edmonton, AB
Canada T6G 2G1

Maryna Yaskina

Department of Mathematical and Statistical Sciences
University of Alberta
Edmonton, AB
Canada T6G 2G1
myaskina@math.ualberta.ca

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.

2000 Mathematics Subject Classification 52A20, 42B10, 33C55.

The second and third authors were supported in part by the European Network PHD, FP6 Marie Curie Actions, RTN, Contract MCRN-511953.

Received November 21, 2007; published online July 29, 2009.


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