Uncertainty Principles, Spectral Localization, and Singular Schrödinger Operators on Compact Manifolds
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866918523043840000 |
|---|---|
| author | Iosevich, Alex Park, Chamsol |
| author_facet | Iosevich, Alex Park, Chamsol |
| contents | We establish uncertainty principles on compact Riemannian manifolds without boundary by combining restriction estimates for orthonormal systems with spectral projection bounds for Laplace-Beltrami and Schrödinger operators. Our results relate the size of the support of spectrally localized functions to the cardinality of the underlying spectral cluster and to Fourier-ratio type quantities. We obtain analogues for Schrödinger operators with singular potentials belonging to Kato and scaling-critical classes. As an application, we prove uniqueness results for recovery from incomplete spectral data on compact manifolds. Under curvature assumptions, including nonpositive and negative sectional curvatures, we also prove logarithmically improved uncertainty principles associated with shrinking spectral windows. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_26264 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Uncertainty Principles, Spectral Localization, and Singular Schrödinger Operators on Compact Manifolds Iosevich, Alex Park, Chamsol Analysis of PDEs Classical Analysis and ODEs Spectral Theory 35P15, 35P20, 35Q40, 58J50 We establish uncertainty principles on compact Riemannian manifolds without boundary by combining restriction estimates for orthonormal systems with spectral projection bounds for Laplace-Beltrami and Schrödinger operators. Our results relate the size of the support of spectrally localized functions to the cardinality of the underlying spectral cluster and to Fourier-ratio type quantities. We obtain analogues for Schrödinger operators with singular potentials belonging to Kato and scaling-critical classes. As an application, we prove uniqueness results for recovery from incomplete spectral data on compact manifolds. Under curvature assumptions, including nonpositive and negative sectional curvatures, we also prove logarithmically improved uncertainty principles associated with shrinking spectral windows. |
| title | Uncertainty Principles, Spectral Localization, and Singular Schrödinger Operators on Compact Manifolds |
| topic | Analysis of PDEs Classical Analysis and ODEs Spectral Theory 35P15, 35P20, 35Q40, 58J50 |
| url | https://arxiv.org/abs/2605.26264 |