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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.00780 |
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| _version_ | 1866912139324686336 |
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| author | Anker, Jean-Philippe Palmirotta, Guendalina Sire, Yannick |
| author_facet | Anker, Jean-Philippe Palmirotta, Guendalina Sire, Yannick |
| contents | We investigate dispersive and Strichartz estimates for the Schrödinger equation involving the fractional Laplacian in real hyperbolic spaces and their discrete analogues, homogeneous trees. Due to the Knapp phenomenon, the Strichartz estimates on Euclidean spaces for the fractional Laplacian exhibit loss of derivatives. A similar phenomenon appears on real hyperbolic spaces. However, such a loss disappears on homogeneous trees, due to the triviality of the estimates for small times. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00780 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Schrödinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees Anker, Jean-Philippe Palmirotta, Guendalina Sire, Yannick Analysis of PDEs We investigate dispersive and Strichartz estimates for the Schrödinger equation involving the fractional Laplacian in real hyperbolic spaces and their discrete analogues, homogeneous trees. Due to the Knapp phenomenon, the Strichartz estimates on Euclidean spaces for the fractional Laplacian exhibit loss of derivatives. A similar phenomenon appears on real hyperbolic spaces. However, such a loss disappears on homogeneous trees, due to the triviality of the estimates for small times. |
| title | The Schrödinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2412.00780 |