Radon transforms over lower-dimensional horospheres in real hyperbolic space

Abstract

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.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1090/tran/7666

Keywords

Horospherical transforms, Inversion formulas, L -spaces p, Radon transforms, Real hyperbolic space

Publication Date

1-1-2019

Journal Title

Transactions of the American Mathematical Society

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