Note on Robins' Conjecture in Dimension Four and Higher
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912709938774016 |
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| author | Asipchuk, Oleg |
| author_facet | Asipchuk, Oleg |
| contents | This article is motivated by a conjecture proposed by Sinai Robins in 2024. The conjecture asserts that two convex, centrally symmetric sets of positive measure that are not multi-tilers must coincide up to rigid motions if and only if their Fourier transforms agree on the lattice $\mathbb{Z}^d$. In this paper, we disprove the conjecture by constructing explicit counterexamples in dimensions $d \geq 4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_26587 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Note on Robins' Conjecture in Dimension Four and Higher Asipchuk, Oleg Functional Analysis 42C15, 42C30 This article is motivated by a conjecture proposed by Sinai Robins in 2024. The conjecture asserts that two convex, centrally symmetric sets of positive measure that are not multi-tilers must coincide up to rigid motions if and only if their Fourier transforms agree on the lattice $\mathbb{Z}^d$. In this paper, we disprove the conjecture by constructing explicit counterexamples in dimensions $d \geq 4$. |
| title | Note on Robins' Conjecture in Dimension Four and Higher |
| topic | Functional Analysis 42C15, 42C30 |
| url | https://arxiv.org/abs/2509.26587 |