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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2212.14330 |
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| _version_ | 1866916407505059840 |
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| author | Cho, Chu-hee Shiraki, Shobu |
| author_facet | Cho, Chu-hee Shiraki, Shobu |
| contents | We study the Hausdorff dimension of the sets on which the pointwise convergence of the solutions to the fractional Schrödinger equation $e^{it(-Δ)^\frac m2}f$ fails when $m\in(0,1)$ in one spatial dimension. The pointwise convergence along a non-tangential curve and a set of lines are also considered, where we find different nature from the case when $m\in(1,\infty)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_14330 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Dimension of divergence sets of oscillatory integrals with concave phase Cho, Chu-hee Shiraki, Shobu Analysis of PDEs Functional Analysis 35Q41 We study the Hausdorff dimension of the sets on which the pointwise convergence of the solutions to the fractional Schrödinger equation $e^{it(-Δ)^\frac m2}f$ fails when $m\in(0,1)$ in one spatial dimension. The pointwise convergence along a non-tangential curve and a set of lines are also considered, where we find different nature from the case when $m\in(1,\infty)$. |
| title | Dimension of divergence sets of oscillatory integrals with concave phase |
| topic | Analysis of PDEs Functional Analysis 35Q41 |
| url | https://arxiv.org/abs/2212.14330 |