Abstract

Ridgelet transforms on spaces of constant curvature

Boris Rubin
Hebrew University, Jerusalem, Israel
Department of Mathematics

We introduce continuous ridgelet transforms on spaces
of constant curvature. These transforms agree with the
corresponding
$k$-dimensional totally geodesic Radon transforms on the
$n$-dimensional real euclidean space, the unit sphere, and
the hyperbolic
space. Various inversion and reproducing formulas are obtained
for continuous and $p$-integrable functions in the maximal
range of the parameter $p$.