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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2308.09846 |
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Table of 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.