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Low-Discrepancy Sequences for Piecewise Smooth Functions on the Torus

  • Luca Brandolini
  • Leonardo Colzani
  • Giacomo GiganteEmail author
  • Giancarlo Travaglini
Chapter

Abstract

We produce low-discrepancy infinite sequences which can be used to approximate the integral of a smooth periodic function restricted to a smooth convex domain with positive curvature in \(\mathbb {R}^{d}\). The proof depends on simultaneous Diophantine approximation and on appropriate estimates of the decay of the Fourier transform of characteristic functions.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Luca Brandolini
    • 1
  • Leonardo Colzani
    • 2
  • Giacomo Gigante
    • 1
    Email author
  • Giancarlo Travaglini
    • 2
  1. 1.Dipartimento di Ingegneria Gestionale, dell’Informazione e della ProduzioneUniversità degli Studi di BergamoDalmineItaly
  2. 2.Dipartimento di Matematica e ApplicazioniUniversità di Milano-BicoccaMilanoItaly

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