When is the fractal uncertainty principle for discrete Cantor sets most uncertain?
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916547423895552 |
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| author | Lai, Chun-Kit Shi, Ruxi |
| author_facet | Lai, Chun-Kit Shi, Ruxi |
| contents | We give a necessary and sufficient condition to achieve the most uncertain exponent in the fractal uncertainty principle of discrete Cantor sets. The condition will be described as distributed spectral pairs, which is a generalization of the spectral pair studied in the spectral sets literature. We investigate distributed spectral pairs in some cyclic groups and some complete classifications are given. Finally, we also discuss the most uncertain case in the continuous setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00864 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | When is the fractal uncertainty principle for discrete Cantor sets most uncertain? Lai, Chun-Kit Shi, Ruxi Classical Analysis and ODEs Functional Analysis We give a necessary and sufficient condition to achieve the most uncertain exponent in the fractal uncertainty principle of discrete Cantor sets. The condition will be described as distributed spectral pairs, which is a generalization of the spectral pair studied in the spectral sets literature. We investigate distributed spectral pairs in some cyclic groups and some complete classifications are given. Finally, we also discuss the most uncertain case in the continuous setting. |
| title | When is the fractal uncertainty principle for discrete Cantor sets most uncertain? |
| topic | Classical Analysis and ODEs Functional Analysis |
| url | https://arxiv.org/abs/2501.00864 |