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arXiv · 2605.29781

Restriction problems on the three-dimensional Heisenberg nilmanifold

Hajer Bahouri·Veronique Fischer
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Abstract

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.

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Hajer Bahouri, Veronique Fischer. 2026-05-28. Restriction problems on the three-dimensional Heisenberg nilmanifold. https://arxiv.org/abs/2605.29781

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