Planar convex bodies, Fourier transform, lattice points, and irregularities of distribution

DOI10.1090/S0002-9947-03-03240-9zbMath1032.42018MaRDI QIDQ4417273

Alexander Iosevich, Luca Brandolini, Giancarlo Travaglini

Publication date: 28 July 2003

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

zbMATH Keywords

lattice pointsconvex bodiesMinkowski dimensionirregularities of distributiondecay of Fourier transforms

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Lattices and convex bodies (number-theoretic aspects) (11H06) Lattice points in specified regions (11P21) Convex sets in (2) dimensions (including convex curves) (52A10)

Related Items (6)

A characterization theorem for the \(L^{2}\)-discrepancy of integer points in dilated polygons ⋮ L p Mixed-norm estimates for convolution operator defined by singular measures ⋮ Effect of window shape on the detection of hyperuniformity via the local number variance ⋮ FREIMAN THEOREM, FOURIER TRANSFORM AND ADDITIVE STRUCTURE OF MEASURES ⋮ Large-degree asymptotics and exponential asymptotics for Fourier, Chebyshev and Hermite coefficients and Fourier transforms ⋮ Irregularities of distribution and geometry of planar convex sets

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Irregularities of distribution. I
• Convex hypersurfaces and Fourier transforms
• Average decay of Fourier transforms and integer points in polyhedra
• An \(H^ 1\) multiplier theorem
• The convex floating body and polyhedral approximation
• Average decay of Fourier transforms and geometry of convex sets
• Pointwise convergence of Fejér type means
• Localization and convergence of eigenfunction expansions
• Convex curves, Radon transforms and convolution operators defined by singular measures
• Irregularities of point distribution relative to convex polygons II
• Note on Irregularities of Distribution II
• Extensions of Hardy spaces and their use in analysis
• On the Number of Lattice Points in a Compact n-Dimensional Polyhedron
• ON THE NUMBER OF LATTICE POINTS INSIDE A RANDOM OVAL
• Riesz means associated with convex domains in the plane

This page was built for publication: Planar convex bodies, Fourier transform, lattice points, and irregularities of distribution