lemma 17.6 Dirichlet kernel

open in the book · parts/02-mathematical-methods/15-fourier-integral-transforms.tex:283 · p. 674

Rests on

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 proposition 17.26 The lattice harmonics are an orthonormal basis ¶
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 ¶

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:300
`depends_on`	→	Orthogonality of the harmonics	declared	parts/02-mathematical-methods/15-fourier-integral-transforms.tex:300
`depends_on`	←	Localisation	declared	parts/02-mathematical-methods/15-fourier-integral-transforms.tex:376
`depends_on`	←	Divergence of the Lebesgue constants	declared	parts/02-mathematical-methods/15-fourier-integral-transforms.tex:538
`depends_on`	←	Dirichlet	declared	parts/02-mathematical-methods/15-fourier-integral-transforms.tex:415
`depends_on`	←	du Bois-Reymond	declared	parts/02-mathematical-methods/15-fourier-integral-transforms.tex:562
`depends_on`	←	Fejér	declared	parts/02-mathematical-methods/15-fourier-integral-transforms.tex:908
`proves`	←	ch:15-fourier-integral-transforms@proof-4	declared	parts/02-mathematical-methods/15-fourier-integral-transforms.tex:303