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Multidimensional Fourier Methods

  • Gerlind Plonka
  • Daniel Potts
  • Gabriele Steidl
  • Manfred Tasche
Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

In this chapter, we consider d-dimensional Fourier methods for fixed \(d\in \mathbb N\). We start with Fourier series of d-variate, 2π-periodic functions \(f:\,\mathbb T^d \to \mathbb C\) in Sect. 4.1, where we follow the lines of Chap.  1. In particular, we present basic properties of the Fourier coefficients and learn about their decay for smooth functions.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Gerlind Plonka
    • 1
  • Daniel Potts
    • 2
  • Gabriele Steidl
    • 3
  • Manfred Tasche
    • 4
  1. 1.University of GöttingenGöttingenGermany
  2. 2.Chemnitz University of TechnologyChemnitzGermany
  3. 3.TU KaiserslauternKaiserslauternGermany
  4. 4.University of RostockRostockGermany

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