Skip to main navigation Skip to search Skip to main content

Totally Geodesic Radon Transform of Lp-Functions on Real Hyperbolic Space

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

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 ftextexclamdownÊLp(Hn), where Hn is the n-dimensional real hyperbolic space, and 1 textexclamdownÜ d textexclamdownÜ n - 1. We show that f is well defined if and only if 1 textexclamdownÜ 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.
Original languageEnglish
Title of host publicationFourier Analysis and Convexity
EditorsLuca Brandolini, Leonardo Colzani, Giancarlo Travaglini, Alex Iosevich
Place of PublicationBoston, MA
PublisherBirkhauser Boston
Pages37-58
Number of pages22
ISBN (Print)978-0-8176-8172-2
DOIs
StatePublished - 2004

Publication series

NameApplied and Numerical Harmonic Analysis

Fingerprint

Dive into the research topics of 'Totally Geodesic Radon Transform of Lp-Functions on Real Hyperbolic Space'. Together they form a unique fingerprint.

Cite this