Fractal uncertainty in higher dimensions
Fuente:
arXiv
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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913532520431616 |
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| author | Cohen, Alex |
| author_facet | Cohen, Alex |
| contents | We prove that if a fractal set in $\mathbb{R}^d$ avoids lines in a certain quantitative sense, which we call line porosity, then it has a fractal uncertainty principle. The main ingredient is a new higher dimensional Beurling-Malliavin multiplier theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_05022 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fractal uncertainty in higher dimensions Cohen, Alex Classical Analysis and ODEs Complex Variables Spectral Theory We prove that if a fractal set in $\mathbb{R}^d$ avoids lines in a certain quantitative sense, which we call line porosity, then it has a fractal uncertainty principle. The main ingredient is a new higher dimensional Beurling-Malliavin multiplier theorem. |
| title | Fractal uncertainty in higher dimensions |
| topic | Classical Analysis and ODEs Complex Variables Spectral Theory |
| url | https://arxiv.org/abs/2305.05022 |