lemma 17.2 Orthogonality of the harmonics

open in the book · parts/02-mathematical-methods/15-fourier-integral-transforms.tex:103 · p. 672

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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 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 ¶ ↺

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Fourier coefficients and Fourier series	declared	parts/02-mathematical-methods/15-fourier-integral-transforms.tex:110
`depends_on`	←	Dirichlet kernel	declared	parts/02-mathematical-methods/15-fourier-integral-transforms.tex:300
`depends_on`	←	Least squares and Bessel's inequality	declared	parts/02-mathematical-methods/15-fourier-integral-transforms.tex:222
`depends_on`	←	Euler–Fourier coefficient formulas	declared	parts/02-mathematical-methods/15-fourier-integral-transforms.tex:142
`depends_on`	←	Parseval's identity for series	declared	parts/02-mathematical-methods/15-fourier-integral-transforms.tex:1381
`proves`	←	ch:15-fourier-integral-transforms@proof-1	declared	parts/02-mathematical-methods/15-fourier-integral-transforms.tex:113