Work

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

Year: 2025

Type: preprint

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.

Source: arXiv (Cornell University)

Authors: Jiang, Yan, Liu, Hongyu, Zhang, Kai, Zheng, Haoran

Institutions: City University of Hong Kong, Jilin University, South China Normal University

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Agence Nationale de la Recherche

Award: G242747065

OpenAlex ID: W7077674760

Cites:

Cited by:

Related to: