proposition 17.4 Least squares and Bessel's inequality

open in the book · parts/02-mathematical-methods/15-fourier-integral-transforms.tex:208 · p. 673

Rests on

depends_on definition 17.1 Fourier coefficients and Fourier series ¶
depends_on lemma 17.2 Orthogonality of the harmonics ¶
- depends_on definition 17.1 Fourier coefficients and Fourier series ¶ ↺
- proves proof ch:15-fourier-integral-transforms@proof-1 ¶
proves proof ch:15-fourier-integral-transforms@proof-3 ¶

Supports

depends_on corollary 17.11 Uniform convergence for $C^{1}$ functions ¶
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 ¶

Neighborhood

Every logical edge within two steps of this node.

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Edges

type	direction	node	provenance	where
`depends_on`	→	Fourier coefficients and Fourier series	declared	parts/02-mathematical-methods/15-fourier-integral-transforms.tex:222
`depends_on`	→	Orthogonality of the harmonics	declared	parts/02-mathematical-methods/15-fourier-integral-transforms.tex:222
`depends_on`	←	Uniform convergence for $C^{1}$ functions	declared	parts/02-mathematical-methods/15-fourier-integral-transforms.tex:502
`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-3	declared	parts/02-mathematical-methods/15-fourier-integral-transforms.tex:225