FREIMAN THEOREM, FOURIER TRANSFORM AND ADDITIVE STRUCTURE OF MEASURES

DOI10.1017/S1446788708000530zbMath1166.42007OpenAlexW1998815415MaRDI QIDQ3624627

Alexander Iosevich, Michael Rudnev

Publication date: 30 April 2009

Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s1446788708000530

zbMATH Keywords

Fourier transformarithmetic progressiondecay estimatesdistance set

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Erd?s problems and related topics of discrete geometry (52C10)

Related Items (3)

Non-central limit theorems for functionals of random fields on hypersurfaces ⋮ Sharpness of Falconer's (d+1)/2 estimate ⋮ Sharpness of Falconer’s Estimate and the Single Distance Problem in $$\mathbb{Z}_{q}^{d}$$

Cites Work

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• Non-isotropic distance measures for lattice-generated sets
• Average decay of Fourier transforms and geometry of convex sets
• Sharp rate of average decay of the Fourier transform of a bounded set
• Erdös distance problem in vector spaces over finite fields
• Planar convex bodies, Fourier transform, lattice points, and irregularities of distribution
• Freiman's theorem in an arbitrary abelian group
• On Sets of Distances of n Points

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