Title

An Inversion Formula For The Dual Horocyclic Radon Transform On The Hyperbolic Plane

Keywords

Dual Radon transform; Horocycle; Hyperbolic plane; Inversion formula

Abstract

Consider the Poincare unit disk model for the hyperbolic plane H 2. Let ξ be the set of all horocycles in H2 parametrized by (θ, p), where eiθ is the point where a horocycle ξ is tangent to the boundary |z| = 1, and p is the hyperbolic distance from ξ to the origin. In this paper we invert the dual Radon transform R*; μ(θ, p)→ μ̌(z) under the assumption of exponential decay of μ and some of its derivatives. The additional assumption is that Pm(d/dp)(μm(p)ep) be even for all m ε Z. Here Pm(d/dp) is a family of differential operators introduced by Helgason, and μm (p) are the coefficients of the Fourier series expansion of μ(θ, p). © 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Publication Date

1-1-2005

Publication Title

Mathematische Nachrichten

Volume

278

Issue

4

Number of Pages

437-450

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1002/mana.200310251

Socpus ID

15944374803 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/15944374803

This document is currently not available here.

Share

COinS