Large sets with limited tube occupancy

Anthony Carbery

doi:10.1112/jlms/jdn086

Large sets with limited tube occupancy

Anthony Carbery

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract / Description of output

We study subsets E of euclidean space with the property that for every tube, the amount of mass of E contained in that tube is small, and address via the probabilistic method the question of how large such sets may be. We also study discrete analogues of this question, and relate it to problems in harmonic analysis concerning the extension operator for the Fourier transform.

Original language	English
Pages (from-to)	529-543
Number of pages	15
Journal	Journal of the London Mathematical Society
Volume	79
Issue number	2
DOIs	https://doi.org/10.1112/jlms/jdn086
Publication status	Published - Apr 2009

Keywords / Materials (for Non-textual outputs)

HEILBRONNS TRIANGLE PROBLEM
LOCALIZATION
ALGORITHM

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10.1112/jlms/jdn086

Large sets with limited tube occupancyFinal published version, 598 KB

http://jlms.oxfordjournals.org/content/79/2/529

Cite this

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title = "Large sets with limited tube occupancy",

abstract = "We study subsets E of euclidean space with the property that for every tube, the amount of mass of E contained in that tube is small, and address via the probabilistic method the question of how large such sets may be. We also study discrete analogues of this question, and relate it to problems in harmonic analysis concerning the extension operator for the Fourier transform.",

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AB - We study subsets E of euclidean space with the property that for every tube, the amount of mass of E contained in that tube is small, and address via the probabilistic method the question of how large such sets may be. We also study discrete analogues of this question, and relate it to problems in harmonic analysis concerning the extension operator for the Fourier transform.

KW - HEILBRONNS TRIANGLE PROBLEM

KW - LOCALIZATION

KW - ALGORITHM

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DO - 10.1112/jlms/jdn086

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JO - Journal of the London Mathematical Society

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ER -

Large sets with limited tube occupancy

Abstract / Description of output

Keywords / Materials (for Non-textual outputs)

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