Spectral properties of surface-localized transmission eigenmodes and applications to inverse scattering problems
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910064090021888 |
|---|---|
| author | Jiang, Yan Liu, Hongyu Zhang, Kai Zheng, Haoran |
| author_facet | Jiang, Yan Liu, Hongyu Zhang, Kai Zheng, Haoran |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_16203 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral properties of surface-localized transmission eigenmodes and applications to inverse scattering problems Jiang, Yan Liu, Hongyu Zhang, Kai Zheng, Haoran Analysis of PDEs 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. |
| title | Spectral properties of surface-localized transmission eigenmodes and applications to inverse scattering problems |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2508.16203 |