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Large sets with limited tube occupancy
Author(s) -
Carbery Anthony
Publication year - 2009
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdn086
Subject(s) - tube (container) , extension (predicate logic) , euclidean space , property (philosophy) , probabilistic logic , fourier transform , occupancy , space (punctuation) , operator (biology) , mathematics , harmonic , computer science , mathematical analysis , statistics , physics , engineering , acoustics , programming language , operating system , architectural engineering , philosophy , biochemistry , chemistry , epistemology , repressor , transcription factor , gene , mechanical engineering
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.