Pointwise Convergence of Schrödinger Operators in Bessel Potential Spaces
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917535990939648 |
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| author | Pan, Yucheng Sun, Wenchang Tan, Jiheng |
| author_facet | Pan, Yucheng Sun, Wenchang Tan, Jiheng |
| contents | We study the pointwise convergence of solutions to the free Schrödinger equation with initial data in the Bessel potential spaces $L_s^p(\mathbb{R}^n)$. We establish new sufficient regularity indices for pointwise convergence across the full range $1 \leq p < \infty$, and demonstrate via counterexamples that these indices are sharp for all $1 \leq p \leq 2$ in one dimension, as well as for $p=1$ or $p$ large enough in higher dimensions. The proofs rely on the high-dimensional stationary phase method. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_25833 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Pointwise Convergence of Schrödinger Operators in Bessel Potential Spaces Pan, Yucheng Sun, Wenchang Tan, Jiheng Analysis of PDEs 46E35, 42B37 We study the pointwise convergence of solutions to the free Schrödinger equation with initial data in the Bessel potential spaces $L_s^p(\mathbb{R}^n)$. We establish new sufficient regularity indices for pointwise convergence across the full range $1 \leq p < \infty$, and demonstrate via counterexamples that these indices are sharp for all $1 \leq p \leq 2$ in one dimension, as well as for $p=1$ or $p$ large enough in higher dimensions. The proofs rely on the high-dimensional stationary phase method. |
| title | Pointwise Convergence of Schrödinger Operators in Bessel Potential Spaces |
| topic | Analysis of PDEs 46E35, 42B37 |
| url | https://arxiv.org/abs/2605.25833 |