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On the Fourier dimension of (d,k)-sets and Kakeya sets with restricted directions
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dc.contributor.author | Fraser, Jonathan | |
dc.contributor.author | Harris, Terence L. J. | |
dc.contributor.author | Kroon, Nicholas G. | |
dc.date.accessioned | 2022-02-28T16:30:20Z | |
dc.date.available | 2022-02-28T16:30:20Z | |
dc.date.issued | 2022-02-24 | |
dc.identifier | 277328025 | |
dc.identifier | 5f222708-1028-4fc1-b996-2fca75127a53 | |
dc.identifier | 000761838600001 | |
dc.identifier | 85125133830 | |
dc.identifier.citation | Fraser , J , Harris , T L J & Kroon , N G 2022 , ' On the Fourier dimension of (d,k)-sets and Kakeya sets with restricted directions ' , Mathematische Zeitschrift , vol. First Online . https://doi.org/10.1007/s00209-022-02971-3 | en |
dc.identifier.issn | 0025-5874 | |
dc.identifier.other | ORCID: /0000-0002-8066-9120/work/109316080 | |
dc.identifier.uri | https://hdl.handle.net/10023/24964 | |
dc.description | Funding: JMF was financially supported by an EPSRC Standard Grant (EP/R015104/1) and a Leverhulme Trust Research Project Grant (RPG-2019-034). | en |
dc.description.abstract | A (d, k)-set is a subset of ℝd containing a k-dimensional unit ball of all possible orientations. Using an approach of D. Oberlin we prove various Fourier dimension estimates for compact (d, k)-sets. Our main interest is in restricted (d, k)-sets, where the set only contains unit balls with a restricted set of possible orientations Γ. In this setting our estimates depend on the Hausdorff dimension of Γ and can sometimes be improved if additional geometric properties of Γ are assumed. We are led to consider cones and prove that the cone in ℝd+1 has Fourier dimension d−1, which may be of interest in its own right. | |
dc.format.extent | 12 | |
dc.format.extent | 277493 | |
dc.language.iso | eng | |
dc.relation.ispartof | Mathematische Zeitschrift | en |
dc.subject | Fourier dimension | en |
dc.subject | Kakeya set | en |
dc.subject | (d, k)-set | en |
dc.subject | Hausdorff dimension | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | On the Fourier dimension of (d,k)-sets and Kakeya sets with restricted directions | en |
dc.type | Journal article | en |
dc.contributor.sponsor | EPSRC | en |
dc.contributor.sponsor | The Leverhulme Trust | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.identifier.doi | https://doi.org/10.1007/s00209-022-02971-3 | |
dc.description.status | Peer reviewed | en |
dc.identifier.grantnumber | EP/R015104/1 | en |
dc.identifier.grantnumber | RPG-2019-034 | en |
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