Radon transforms over lower-dimensional horospheres in real hyperbolic space

William O. Bray; Boris Rubin

doi:10.1090/tran/7666

Radon transforms over lower-dimensional horospheres in real hyperbolic space

William O. Bray, Boris Rubin

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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 L^p. The case d = n 1 agrees with the well-known Gelfand-Graev transform.

Original language	English
Pages (from-to)	1091-1112
Number of pages	22
Journal	Transactions of the American Mathematical Society
Volume	372
Issue number	2
DOIs	https://doi.org/10.1090/tran/7666
State	Published - 2019
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2019 American Mathematical Society.

Keywords

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

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10.1090/tran/7666

Cite this

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AB - 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.

KW - Horospherical transforms

KW - Inversion formulas

KW - L-spaces

KW - Radon transforms

KW - Real hyperbolic space

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ER -

Radon transforms over lower-dimensional horospheres in real hyperbolic space

Abstract

Bibliographical note

Keywords

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