Fredholm Theory of Non-Elliptic Operators in the Presence of Normally Hyperbolic Trapping
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909856307347456 |
|---|---|
| author | Amar, Selim |
| author_facet | Amar, Selim |
| contents | We present an improved Fredholm theory of non-elliptic operators for when the corresponding classical dynamical system exhibits normally hyperbolic trapping with smooth backward and forward trapped sets. It takes place on coisotropic Sobolev spaces with weak regularity at the backward trapped set $Γ_u$, which are roughly speaking made of distributions $v \in H^s$ satisfying $Φ_u v \in H^{s+1}$ for some quantization $Φ_u$ of the defining function $ϕ_u$ of $Γ_u$. We then apply it to the case of wave operators on spacetimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_16642 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fredholm Theory of Non-Elliptic Operators in the Presence of Normally Hyperbolic Trapping Amar, Selim Analysis of PDEs 35L05 (Primary) 35P25, 58J47, 83C57 (Secondary) We present an improved Fredholm theory of non-elliptic operators for when the corresponding classical dynamical system exhibits normally hyperbolic trapping with smooth backward and forward trapped sets. It takes place on coisotropic Sobolev spaces with weak regularity at the backward trapped set $Γ_u$, which are roughly speaking made of distributions $v \in H^s$ satisfying $Φ_u v \in H^{s+1}$ for some quantization $Φ_u$ of the defining function $ϕ_u$ of $Γ_u$. We then apply it to the case of wave operators on spacetimes. |
| title | Fredholm Theory of Non-Elliptic Operators in the Presence of Normally Hyperbolic Trapping |
| topic | Analysis of PDEs 35L05 (Primary) 35P25, 58J47, 83C57 (Secondary) |
| url | https://arxiv.org/abs/2510.16642 |