Radon Transforms over Lower-Dimensional Horospheres in Real Hyperbolic Space
Bray, W. O. · Rubin, B.
Original · EN
We study horospherical Radon transforms that integrate functions on the n-dimensional real hyperbolic space over horospheres of arbitrary fixed dimension 1≤ d≤ n-1. Exact existence conditions and new explicit inversion formulas are obtained for these transforms acting on smooth functions and functions belonging to Lᵖ. The case d=n-1 agrees with the well-known Gelfand-Graev transform.
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