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In this paper we study the Radon transform on the set of horocycles of a homogeneous tree , and describe its image on various function spaces. We show that the functions of compact support on that satisfy two explicit Radon conditions constitute the image under of functions of finite support on . We extend these results to spaces of functions with suitable decay on , whose image under satisfies corresponding decay conditions and contains distributions on that are not defined pointwise....
We prove that ridgelet transform and adjoint ridgelet transform are continuous, where . We also define the ridgelet transform on the space of tempered distributions on , adjoint ridgelet transform on and establish that they are linear, continuous with respect to the weak-topology, consistent with , respectively, and they satisfy the identity , .
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