#### Title

An inversion formula for the dual horocyclic Radon transform on the hyperbolic plane

#### Abbreviated Journal Title

Math. Nachr.

#### Keywords

dual Radon transform; horocycle; hyperbolic plane; inversion formula; CONSTANT CURVATURE; SPACES; Mathematics

#### Abstract

Consider the Poincare unit disk model for the hyperbolic plane H-2. Let Xi be the set of all horocycles in H 2 parametrized by (theta, p), where e(i theta) is the point where a horocycle xi is tangent to the boundary vertical bar z vertical bar = 1, and p is the hyperbolic distance from xi to the origin. In this paper we invert the dual Radon transform R* : mu(theta, p) - > mu(z) under the assumption of exponential decay of mu and some of its derivatives. The additional assumption is that P-m(d/dp) (mu(m)(p)e(p)) be even for all m is an element of Z. Here P-m (d/dp) is a family of differential operators introduced by Helgason, and mu(m) (p) are the coefficients of the Fourier series expansion of mu(theta, p). (c) 2005 WILEY-VCH Verlag GmbH C Co.

#### Journal Title

Mathematische Nachrichten

#### Volume

278

#### Issue/Number

4

#### Publication Date

1-1-2005

#### Document Type

Article

#### Language

English

#### First Page

437

#### Last Page

450

#### WOS Identifier

#### ISSN

0025-584X

#### Recommended Citation

"An inversion formula for the dual horocyclic Radon transform on the hyperbolic plane" (2005). *Faculty Bibliography 2000s*. 5329.

https://stars.library.ucf.edu/facultybib2000/5329

## Comments

Authors: contact us about adding a copy of your work at STARS@ucf.edu