Spectral synthesis on Riemannian manifolds
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866917356856410112 |
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| author | Iosevich, A. Mayeli, A. Wyman, E. |
| author_facet | Iosevich, A. Mayeli, A. Wyman, E. |
| contents | We study spectral synthesis for measures supported on thin subsets of compact Riemannian manifolds. We prove that under natural non-concentration conditions, such measures admit quantitative spectral synthesis, with explicit stability bounds.
We show that this phenomenon depends strongly on the underlying geometry. On the torus, synthesis holds under broad assumptions, while on the sphere we establish rigidity results demonstrating that synthesis can fail in a sharp sense.
As consequences, we obtain quantitative approximation results and uncertainty principles for functions with thin spectral support. These results provide a unified framework connecting spectral synthesis, geometric structure, and stability on compact manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21451 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral synthesis on Riemannian manifolds Iosevich, A. Mayeli, A. Wyman, E. Classical Analysis and ODEs Analysis of PDEs Spectral Theory 42A65, 58J51 We study spectral synthesis for measures supported on thin subsets of compact Riemannian manifolds. We prove that under natural non-concentration conditions, such measures admit quantitative spectral synthesis, with explicit stability bounds. We show that this phenomenon depends strongly on the underlying geometry. On the torus, synthesis holds under broad assumptions, while on the sphere we establish rigidity results demonstrating that synthesis can fail in a sharp sense. As consequences, we obtain quantitative approximation results and uncertainty principles for functions with thin spectral support. These results provide a unified framework connecting spectral synthesis, geometric structure, and stability on compact manifolds. |
| title | Spectral synthesis on Riemannian manifolds |
| topic | Classical Analysis and ODEs Analysis of PDEs Spectral Theory 42A65, 58J51 |
| url | https://arxiv.org/abs/2603.21451 |