Strichartz's conjecture for the spinor bundle over the real hyperbolic space
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910774055665664 |
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| author | Boussejra, Abdelhamid Koufany, Khalid |
| author_facet | Boussejra, Abdelhamid Koufany, Khalid |
| contents | Let $H^n(\mathbb R)$ denote the real hyperbolic space realized as the symmetric space $Spin_0(1,n)/Spin(n)$. In this paper, we provide a characterization for the image of the Poisson transform for $L^2$-sections of the spinor bundle over the boundary ${\partial H}^n(\mathbb R)$. As a consequence, we obtain an $L^2$ uniform estimate for the generalized spectral projections associated to the spinor bundle over $H^n(\mathbb R)$, thereby extending Strichartz's conjecture from the scalar case to the spinor setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03351 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strichartz's conjecture for the spinor bundle over the real hyperbolic space Boussejra, Abdelhamid Koufany, Khalid Representation Theory Differential Geometry 43A90, 43A85, 58J50, 15A66 Let $H^n(\mathbb R)$ denote the real hyperbolic space realized as the symmetric space $Spin_0(1,n)/Spin(n)$. In this paper, we provide a characterization for the image of the Poisson transform for $L^2$-sections of the spinor bundle over the boundary ${\partial H}^n(\mathbb R)$. As a consequence, we obtain an $L^2$ uniform estimate for the generalized spectral projections associated to the spinor bundle over $H^n(\mathbb R)$, thereby extending Strichartz's conjecture from the scalar case to the spinor setting. |
| title | Strichartz's conjecture for the spinor bundle over the real hyperbolic space |
| topic | Representation Theory Differential Geometry 43A90, 43A85, 58J50, 15A66 |
| url | https://arxiv.org/abs/2501.03351 |