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arXiv · 2601.11146

Inverse Spectral Problem With Low Regularity Refractive Index

Kewen Bu·Youjun Deng·Yan Jiang·Kai Zhang
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Abstract

This article investigates the unique determination of a radial refractive index n from spectral data. First, we demonstrate that for piecewise twice continuously differentiable functions, n is not uniquely determined by the special transmission eigenvalues associated with radially symmetric eigenfunctions. Subsequently we prove that if n \in M is twice continuously differentiable functions(or continuously differentiable functions with Lipschitz continuous derivative), then n is uniquely determined on [0,1] by all special transmission eigenvalues when supplemented by partial a priori information on the refractive index.

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Kewen Bu, Youjun Deng, Yan Jiang, Kai Zhang. 2026-01-16. Inverse Spectral Problem With Low Regularity Refractive Index. https://arxiv.org/abs/2601.11146

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