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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.06302 |
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| _version_ | 1866929586268274688 |
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| author | Cruz, Angel D. |
| author_facet | Cruz, Angel D. |
| contents | We consider a translation invariant linear equation in four variables with integer coefficients of the form: $ax_1 +bx_2= cy_1+dy_2$. The main result of the paper states that any set on the real line with Fourier dimension greater than 1/2 must contain a nontrivial solution of such an equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06302 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fourier Dimension and Translation Invariant Linear Equations Cruz, Angel D. Classical Analysis and ODEs We consider a translation invariant linear equation in four variables with integer coefficients of the form: $ax_1 +bx_2= cy_1+dy_2$. The main result of the paper states that any set on the real line with Fourier dimension greater than 1/2 must contain a nontrivial solution of such an equation. |
| title | Fourier Dimension and Translation Invariant Linear Equations |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2411.06302 |