The Fourier spectrum and sumset type problems
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Accesso online: | |
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| _version_ | 1866916051081494528 |
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| author | Fraser, Jonathan M. |
| author_facet | Fraser, Jonathan M. |
| contents | We introduce and study the \emph{Fourier spectrum} which is a continuously parametrised family of dimensions living between the Fourier dimension and the Hausdorff dimension for both sets and measures. We establish some fundamental theory and motivate the concept via several applications, especially to sumset type problems. For example, we study dimensions of convolutions and sumsets, and solve the distance set problem for sets satisfying certain Fourier analytic conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_07019 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Fourier spectrum and sumset type problems Fraser, Jonathan M. Classical Analysis and ODEs Dynamical Systems Functional Analysis Metric Geometry Probability primary: 42B10, 28A80, secondary: 28A75, 28A78 We introduce and study the \emph{Fourier spectrum} which is a continuously parametrised family of dimensions living between the Fourier dimension and the Hausdorff dimension for both sets and measures. We establish some fundamental theory and motivate the concept via several applications, especially to sumset type problems. For example, we study dimensions of convolutions and sumsets, and solve the distance set problem for sets satisfying certain Fourier analytic conditions. |
| title | The Fourier spectrum and sumset type problems |
| topic | Classical Analysis and ODEs Dynamical Systems Functional Analysis Metric Geometry Probability primary: 42B10, 28A80, secondary: 28A75, 28A78 |
| url | https://arxiv.org/abs/2210.07019 |