A characterization of the $L^2$-range of the generalized spectral projections related to the Hodge-de Rham Laplacian
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913475029106688 |
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| author | Boussejra, Abdelhamid Koufany, Khalid |
| author_facet | Boussejra, Abdelhamid Koufany, Khalid |
| contents | Let $H^n(\mathbb R)$ be the real hyperbolic space. In this paper, we present a characterization of the $L^2$-range of the generalized spectral projections on the bundle of differential forms over $H^n(\mathbb R)$. As an underlying result we show a characterization of the $L^2$-range of the Poisson transform on the bundle of differential forms on the boundary $\partial H^n(\mathbb R)$. This gives a positive answer to a conjecture of Strichartz on differential forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_00536 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A characterization of the $L^2$-range of the generalized spectral projections related to the Hodge-de Rham Laplacian Boussejra, Abdelhamid Koufany, Khalid Representation Theory 43A90, 43A85, 58J50 Let $H^n(\mathbb R)$ be the real hyperbolic space. In this paper, we present a characterization of the $L^2$-range of the generalized spectral projections on the bundle of differential forms over $H^n(\mathbb R)$. As an underlying result we show a characterization of the $L^2$-range of the Poisson transform on the bundle of differential forms on the boundary $\partial H^n(\mathbb R)$. This gives a positive answer to a conjecture of Strichartz on differential forms. |
| title | A characterization of the $L^2$-range of the generalized spectral projections related to the Hodge-de Rham Laplacian |
| topic | Representation Theory 43A90, 43A85, 58J50 |
| url | https://arxiv.org/abs/2406.00536 |