@inbook{dd378f2dbfbc4e8ab9f711d8db7b2d62,
title = "Totally Geodesic Radon Transform of Lp-Functions on Real Hyperbolic Space",
abstract = "We present a brief discussion of the interrelations between integral geometry and harmonic analysis and then proceed to the d-dimensional totally geodesic Radon transform f, assuming ftextexclamdown{\^E}Lp(Hn), where Hn is the n-dimensional real hyperbolic space, and 1 textexclamdown{\"U} d textexclamdown{\"U} n - 1. We show that f is well defined if and only if 1 textexclamdown{\"U} p < (n -1)/(d - 1) and prove estimates of the Solmon type. By making use of the convolution-backprojection method, approximation to the identity, and the corresponding wavelet-like transforms, we obtain new approximate and explicit inversion formulas for f.",
author = "Berenstein, \{Carlos A.\} and Boris Rubin",
year = "2004",
doi = "10.1007/978-0-8176-8172-2\_2",
language = "אנגלית",
isbn = "978-0-8176-8172-2",
series = "Applied and Numerical Harmonic Analysis",
publisher = "Birkhauser Boston",
pages = "37--58",
editor = "Luca Brandolini and Leonardo Colzani and Giancarlo Travaglini and Alex Iosevich",
booktitle = "Fourier Analysis and Convexity",
address = "ארצות הברית",
}