definition 17.1 Fourier coefficients and Fourier series

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• depends_on definition 17.25 Multiple Fourier series ¶
  • depends_on proposition 17.26 The lattice harmonics are an orthonormal basis ¶
• depends_on lemma 17.6 Dirichlet kernel ¶
  • depends_on corollary 17.8 Localisation ¶
  • depends_on lemma 17.12 Divergence of the Lebesgue constants ¶
    • depends_on theorem 17.13 du Bois-Reymond ¶
  • depends_on theorem 17.9 Dirichlet ¶
    • depends_on corollary 17.11 Uniform convergence for $C^{1}$ functions ¶
    • depends_on theorem 17.47 Poisson summation ¶
      • depends_on corollary 17.81 Sampling periodises the spectrum; aliasing ¶
      • depends_on corollary 17.49 Lattice sums and the reciprocal lattice ¶
        • depends_on definition 17.25 Multiple Fourier series ¶ ↺
  • depends_on theorem 17.13 du Bois-Reymond ¶ ↺
  • depends_on theorem 17.22 Fejér ¶
    • depends_on corollary 17.23 Density, uniqueness, and no overshoot ¶
    • depends_on proposition 17.26 The lattice harmonics are an orthonormal basis ¶ ↺
    • depends_on theorem 17.34 Parseval's identity for series ¶
      • depends_on proposition 28.48 Modal energy ¶
      • depends_on theorem 17.80 Sampling theorem ¶
        • depends_on corollary 17.107 How many projections ¶
• depends_on lemma 17.2 Orthogonality of the harmonics ¶
  • depends_on lemma 17.6 Dirichlet kernel ¶ ↺
  • depends_on proposition 17.4 Least squares and Bessel's inequality ¶
    • depends_on corollary 17.11 Uniform convergence for $C^{1}$ functions ¶ ↺
    • depends_on theorem 17.34 Parseval's identity for series ¶ ↺
  • depends_on theorem 17.3 Euler–Fourier coefficient formulas ¶
    • depends_on proposition 28.47 Modal solution of the initial-value problem ¶
  • depends_on theorem 17.34 Parseval's identity for series ¶ ↺
• depends_on lemma 17.15 A polynomial whose partial sum spikes at the origin ¶
  • depends_on proposition 17.16 An explicit continuous function with a divergent Fourier series ¶
• depends_on proposition 17.4 Least squares and Bessel's inequality ¶ ↺
• depends_on proposition 17.10 Smoothness and coefficient decay ¶
  • depends_on corollary 17.11 Uniform convergence for $C^{1}$ functions ¶ ↺
• depends_on proposition 17.86 The DFT is exact for a band-limited periodic signal ¶
• depends_on proposition 17.16 An explicit continuous function with a divergent Fourier series ¶ ↺
• depends_on theorem 17.3 Euler–Fourier coefficient formulas ¶ ↺
• depends_on theorem 17.47 Poisson summation ¶ ↺
• depends_on theorem 17.80 Sampling theorem ¶ ↺