Unique continuation properties for the continuous Anderson operator in dimension 2
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909604451975168 |
|---|---|
| author | Moench, Nicolas |
| author_facet | Moench, Nicolas |
| contents | We consider singular continuous Anderson operators $H=Δ+ξ$ on closed manifolds of dimension 1 and 2, and prove a unique continuation property for its eigenfunctions using the theory of quasi-conformal mappings. We investigate its nodal set by proving that it is quasi-conformal to the nodal set of a Laplace eigenfunction and prove a Courant nodal theorem. We also present an application to control for singular operator in dimension 1. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04774 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unique continuation properties for the continuous Anderson operator in dimension 2 Moench, Nicolas Probability We consider singular continuous Anderson operators $H=Δ+ξ$ on closed manifolds of dimension 1 and 2, and prove a unique continuation property for its eigenfunctions using the theory of quasi-conformal mappings. We investigate its nodal set by proving that it is quasi-conformal to the nodal set of a Laplace eigenfunction and prove a Courant nodal theorem. We also present an application to control for singular operator in dimension 1. |
| title | Unique continuation properties for the continuous Anderson operator in dimension 2 |
| topic | Probability |
| url | https://arxiv.org/abs/2505.04774 |