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arXiv · 2508.16203

Spectral properties of surface-localized transmission eigenmodes and applications to inverse scattering problems

Yan Jiang·Hongyu Liu·Kai Zhang·Haoran Zheng
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Abstract

This paper investigates a distinctive spectral pattern exhibited by transmission eigenfunctions in wave scattering theory. Building upon the discovery in [7, 8] that these eigenfunctions localize near the domain boundary, we derive sharp spectral density estimates--establishing both lower and upper bounds--to demonstrate that a significant proportion of transmission eigenfunctions manifest this surface-localizing behavior. Our analysis elucidates the connection between the geometric rigidity of eigenfunctions and their spectral properties. Though primarily explored within a radially symmetric framework, this study provides rigorous theoretical insights, advances new perspectives in this emerging field, and offers meaningful implications for inverse scattering theory.

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Yan Jiang, Hongyu Liu, Kai Zhang, Haoran Zheng. 2025-08-22. Spectral properties of surface-localized transmission eigenmodes and applications to inverse scattering problems. https://arxiv.org/abs/2508.16203

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