Average decay of Fourier transforms and integer points in polyhedra

DOI10.1007/BF02559969zbMath0937.11043OpenAlexW2009174488MaRDI QIDQ1127028

Giancarlo Travaglini, Luca Brandolini, Leonardo Colzani

Publication date: 8 November 1998

Published in: Arkiv för Matematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02559969

zbMATH Keywords

Fourier transformspolyhedralattice pointslattice restdiscrepancyaverage number

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Lattice points in specified regions (11P21)

Related Items

A characterization theorem for the \(L^{2}\)-discrepancy of integer points in dilated polygons, Discrepancy for randomized Riemann sums, Pointwise convergence of Fejér type means, Irregularities of distribution for bounded sets and half‐spaces, DISCREPANCY OF A CONVEX SET WITH ZERO CURVATURE AT ONE POINT, TIGHTER BOUNDS FOR THE DISCREPANCY OF BOXES AND POLYTOPES, Low-Discrepancy Sequences for Piecewise Smooth Functions on the Torus, Mixed $L^{p}(L^{2})$ norms of the lattice point discrepancy, Unnamed Item, Spherical means and the restriction phenomenon, Lattice points and generalized Diophantine conditions, Planar convex bodies, Fourier transform, lattice points, and irregularities of distribution, Mean square decay of Fourier transforms in Euclidean and non Euclidean spaces, Lattice points in algebraic cross-polytopes and simplices, Low-discrepancy sequences for piecewise smooth functions on the two-dimensional torus, Trigonometric approximation and a general form of the Erdős Turán inequality, Unnamed Item, Pseudo-differential operators with discontinuous symbols: Widom’s Conjecture, Irregularities of distribution and geometry of planar convex sets, Deterministic and probabilistic discrepancies, Distribution of values of quadratic forms at integral points

Cites Work

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• On the Number of Lattice Points in a Compact n-Dimensional Polyhedron
• On the Fourier Transform of the Indicator Function of a Planar Set
• ON THE NUMBER OF LATTICE POINTS INSIDE A RANDOM OVAL
• On integer points in polygons