# The Radon Transform on Function Spaces Related to Homogenous Spaces

## TL;DR

This paper investigates the invertibility of the Radon transform and its dual on specific function spaces, introduces new spaces where the transform is bijective, and provides a reconstruction formula with an illustrative example.

## Contribution

It introduces new function spaces for the Radon transform where it acts as a bijective linear operator and derives a reconstruction formula.

## Key findings

- Radon transform is invertible on certain function spaces
- A reconstruction formula for the Radon transform is established
- An example supports the theoretical results

## Abstract

We are going to study some conditions on which the Radon transform and its dual are invertible. Two function spaces are introduced that the Radon transform on which is bijective linear operator. In this regards, a reconstruction formula is constructed. Finally the results are supported by an example.