Work

A Unified Range Characterization for the Spherical mean transform

Year: 2026

Type: preprint

Abstract: In this article, we investigate the range characterization for the spherical mean transform (SMT) of functions supported in the unit ball. In earlier works, in the case of odd dimensions, a set of differential conditions was obtained, whereas in the case of even dimensions, integral conditions were obtained. We prove that these conditions that are different based on the parity of dimension are, in fact, equivalent in odd dimensions. This equivalence shows that the integral conditions yield a unified simple range characterization for the SMT that is valid in both even and odd dimensions.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2605.27034

Authors: Chatterjee, Pradipta, Singhal, Nisha, Tushir, Abhilash

Institution: Tata Institute of Fundamental Research

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Arthritis National Research Foundation, National Research Foundation, Department of Atomic Energy, Government of India

OpenAlex ID: W7162501013

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