Radon Transform over Tensor Fields: Injectivity, Range, and Unique Continuation Principle

TL;DR

This paper investigates the mathematical properties of Radon transforms on tensor fields, including injectivity, range, and unique continuation, extending classical results to more general geometric contexts.

Contribution

It provides a comprehensive analysis of Radon transforms on symmetric tensor fields, revealing their analytic structure and extending classical integral geometry results.

Findings

Radon transforms on tensor fields have a coherent analytic structure.

The study extends classical Radon transform properties to tensor ray transforms.

Results include injectivity, range characterization, and unique continuation principles.

Abstract

A central objective in inverse problems arising in integral geometry is to understand the kernel characterization, inversion formulas, stability estimates, range characterization, and unique continuation properties of integral transforms. In this paper, we study all these aspects for Radon transforms acting on symmetric $m$-tensor fields in $\mathbb{R}^n$. Our results show that these transforms admit a coherent analytic structure, extending several key features of the classical Radon transform and tensor ray transforms to a broader geometric setting.