Abstract
Ridgelet transforms on spaces
of constant curvature
Boris Rubin
Hebrew University, Jerusalem, Israel
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 $p$.
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 $p$.
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