Radon transformation on reductive symmetric spaces: support theorems

TL;DR

This paper introduces Radon transforms on reductive symmetric spaces, including horospherical transforms, and proves a support theorem that generalizes Helgason's classical result for Riemannian symmetric spaces.

Contribution

It extends the theory of Radon transforms to a broader class of symmetric spaces and establishes a generalized support theorem.

Findings

Established a support theorem for Radon transforms on reductive symmetric spaces.

Generalized Helgason's support theorem to a wider class of spaces.

Analyzed properties of horospherical and other Radon transforms.

Abstract

We introduce a class of Radon transforms for reductive symmetric spaces, including the horospherical transforms, and study some of their properties. In particular we obtain a support theorem that generalizes Helgason's support theorem for the horospherical transform on a Riemannian symmetric space.