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The Radon transform on ${\rm SL}(2,{\bf R})/{\rm SO}(2,{\bf R})$
1986
Transactions of the American Mathematical Society
Let G be SL(2,R). G acts on the upper half-plane U by the Möbius transformation, providing M with the Riemannian metric structure along with the Laplacian, A. We study the integral transform along each geodesic. G acts on P, the space of all geodesies, in a natural way, providing P with its invariant measure and its own Laplacian. (P actually is a coset space of G.) Therefore the above transform can be viewed as a map from a suitable function space on M to a suitable function space on P. We
doi:10.1090/s0002-9947-1986-0849481-7
fatcat:sc3wrxoikvepdctydtjdwhxxwy