Improved $L^\infty$ bounds for eigenfunctions under random perturbations in negative curvature
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909498482884608 |
|---|---|
| author | Ingremeau, Maxime Vogel, Martin |
| author_facet | Ingremeau, Maxime Vogel, Martin |
| contents | It has been known since the work of Avakumovíc, Hörmander and Levitan that, on any compact smooth Riemannian manifold, if $-Δ_g ψ_λ= λψ_λ$, then $\|ψ_λ\|_{L^\infty} \leq C λ^{\frac{d-1}{4}} \|ψ_λ\|_{L^2}$. It is believed that, on manifolds of negative curvature, such a bound can be largely improved; however, only logarithmic improvements in $λ$ have been obtained so far. In the present paper, we obtain polynomial improvements over the previous bound in a generic setting, by adding a small random pseudodifferential perturbation to the Laplace-Beltrami operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13739 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Improved $L^\infty$ bounds for eigenfunctions under random perturbations in negative curvature Ingremeau, Maxime Vogel, Martin Spectral Theory Mathematical Physics Analysis of PDEs It has been known since the work of Avakumovíc, Hörmander and Levitan that, on any compact smooth Riemannian manifold, if $-Δ_g ψ_λ= λψ_λ$, then $\|ψ_λ\|_{L^\infty} \leq C λ^{\frac{d-1}{4}} \|ψ_λ\|_{L^2}$. It is believed that, on manifolds of negative curvature, such a bound can be largely improved; however, only logarithmic improvements in $λ$ have been obtained so far. In the present paper, we obtain polynomial improvements over the previous bound in a generic setting, by adding a small random pseudodifferential perturbation to the Laplace-Beltrami operator. |
| title | Improved $L^\infty$ bounds for eigenfunctions under random perturbations in negative curvature |
| topic | Spectral Theory Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2403.13739 |