Restriction problems on the three-dimensional Heisenberg nilmanifold
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914613405155328 |
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| author | Bahouri, Hajer Fischer, Veronique |
| author_facet | Bahouri, Hajer Fischer, Veronique |
| contents | In this paper, we prove a spectral restriction theorem on the three-dimensional Heisenberg nilmanifold. Since this manifold is an $\mathbb S^1$-bundle over the flat torus $\mathbb T^2$, the result provides a sub-elliptic counterpart of Zygmund's restriction theorem on $\mathbb T^2$ \cite{zygmund}. We also establish its sharpness by means of the discrete short-time Fourier transform. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_29781 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Restriction problems on the three-dimensional Heisenberg nilmanifold Bahouri, Hajer Fischer, Veronique Classical Analysis and ODEs Functional Analysis Spectral Theory 43A80, 58J50, 35H20, 42B10, 43A30 In this paper, we prove a spectral restriction theorem on the three-dimensional Heisenberg nilmanifold. Since this manifold is an $\mathbb S^1$-bundle over the flat torus $\mathbb T^2$, the result provides a sub-elliptic counterpart of Zygmund's restriction theorem on $\mathbb T^2$ \cite{zygmund}. We also establish its sharpness by means of the discrete short-time Fourier transform. |
| title | Restriction problems on the three-dimensional Heisenberg nilmanifold |
| topic | Classical Analysis and ODEs Functional Analysis Spectral Theory 43A80, 58J50, 35H20, 42B10, 43A30 |
| url | https://arxiv.org/abs/2605.29781 |