Support Theorems for Horocycles on Hyperbolic Spaces

TL;DR

This paper proves a support theorem for the horocycle Radon transform in hyperbolic spaces, showing how support properties of the transform relate to the original function's support.

Contribution

It introduces a variation of the support theorem where the transform's support is outside a fixed horocycle, extending previous results.

Findings

Support of the horocycle Radon transform outside a horocycle implies the original function's support is outside the same horocycle.

The theorem generalizes classical support theorems to a new geometric setting.

Provides mathematical foundation for inverse problems involving horocycle transforms.

Abstract

A support theorem for the horocycle Radon transform f \to \hat{f} is a property of the form \hat{f} of compact support \rightarrow f of compact support. Here we prove a variation of this result where support (\hat{f}) is outside a fixed horocycle in hyperbolic space.