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| Format: | Preprint |
| Publié: |
2023
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2308.09846 |
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| _version_ | 1866908330035773440 |
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| author | Shmerkin, Pablo |
| author_facet | Shmerkin, Pablo |
| contents | We prove inverse theorems for the size of sumsets and the $L^q$ norms of convolutions in the discretized setting, extending to arbitrary dimension an earlier result of the author in the line. These results have applications to the dimensions of dynamical self-similar sets and measures, and to the higher dimensional fractal uncertainty principle. The proofs are based on a structure theorem for the entropy of convolution powers due to M.~Hochman. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_09846 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Inverse theorems for discretized sums and $L^q$ norms of convolutions in $\mathbb{R}^d$ Shmerkin, Pablo Classical Analysis and ODEs Combinatorics Dynamical Systems 28A80 (Primary), 11B30, 42B10 (Secondary) We prove inverse theorems for the size of sumsets and the $L^q$ norms of convolutions in the discretized setting, extending to arbitrary dimension an earlier result of the author in the line. These results have applications to the dimensions of dynamical self-similar sets and measures, and to the higher dimensional fractal uncertainty principle. The proofs are based on a structure theorem for the entropy of convolution powers due to M.~Hochman. |
| title | Inverse theorems for discretized sums and $L^q$ norms of convolutions in $\mathbb{R}^d$ |
| topic | Classical Analysis and ODEs Combinatorics Dynamical Systems 28A80 (Primary), 11B30, 42B10 (Secondary) |
| url | https://arxiv.org/abs/2308.09846 |