In the hyperbolic disc (or, more generally, in real hyperbolic spaces) we consider the horocyclic Radon transform R and the geodesic Radon transform X. Composition with their respective adjoint operators yields two convolution operators on the disc (with respect to the hyperbolic measure). We describe their convolution kernels in comparison with those of the corresponding operators on a homogeneous tree.
Berenstein, C.a., Tarabusi, E.c., Cohen, J.m., Picardello, A.m. (1991). Integral Geometry on Trees. AMERICAN JOURNAL OF MATHEMATICS, 113(3), 441-470 [10.2307/2374835].
Integral Geometry on Trees
Picardello, A. M.
1991-01-01
Abstract
In the hyperbolic disc (or, more generally, in real hyperbolic spaces) we consider the horocyclic Radon transform R and the geodesic Radon transform X. Composition with their respective adjoint operators yields two convolution operators on the disc (with respect to the hyperbolic measure). We describe their convolution kernels in comparison with those of the corresponding operators on a homogeneous tree.File in questo prodotto:
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