Regularity of Solution of the Schrödinger Equation on Symmetric Space
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913575373635584 |
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| author | Kumar, Pratyoosh Sajjan, Manali |
| author_facet | Kumar, Pratyoosh Sajjan, Manali |
| contents | In this article, we investigate the behavior of solutions \( u(x,t) \) to the fractional Schrödinger equation on rank symmetric spaces of non-compact type. We proved that as time \( t \) approaches $0$, then $u(x,t)$ converges pointwise almost everywhere to the initial radial data \( f \), provided that \( f \in H^s(\mathbb{X}) \) with \( s > \frac{1}{2} \). This result extends Sjölin's results in this setting. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_06104 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Regularity of Solution of the Schrödinger Equation on Symmetric Space Kumar, Pratyoosh Sajjan, Manali Analysis of PDEs In this article, we investigate the behavior of solutions \( u(x,t) \) to the fractional Schrödinger equation on rank symmetric spaces of non-compact type. We proved that as time \( t \) approaches $0$, then $u(x,t)$ converges pointwise almost everywhere to the initial radial data \( f \), provided that \( f \in H^s(\mathbb{X}) \) with \( s > \frac{1}{2} \). This result extends Sjölin's results in this setting. |
| title | Regularity of Solution of the Schrödinger Equation on Symmetric Space |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2411.06104 |