definition 17.25 Multiple Fourier series

open in the book · parts/02-mathematical-methods/15-fourier-integral-transforms.tex:994 · p. 683

ground object -- no derivation owed

Rests on

depends_on corollary 17.49 Lattice sums and the reciprocal lattice ¶
- depends_on definition 17.29 Fourier transform; the treatise convention ¶
- depends_on theorem 17.47 Poisson summation ¶
  - depends_on definition 17.1 Fourier coefficients and Fourier series ¶
  - depends_on definition 17.29 Fourier transform; the treatise convention ¶ ↺
  - depends_on theorem 17.9 Dirichlet ¶
    - depends_on lemma 17.6 Dirichlet kernel ¶
      - depends_on definition 17.1 Fourier coefficients and Fourier series ¶ ↺
      - depends_on lemma 17.2 Orthogonality of the harmonics ¶
      - proves proof ch:15-fourier-integral-transforms@proof-4 ¶
    - depends_on lemma 17.7 Riemann–Lebesgue ¶
      - depends_on definition 7.39 Darboux sums and the definite integral ¶
      - proves proof ch:15-fourier-integral-transforms@proof-5 ¶
    - depends_on theorem 7.35 Mean value theorem ¶
      - depends_on proposition 7.29 Linearity ¶
      - depends_on theorem 7.34 Rolle ¶
      - proves proof ch:05-real-analysis@proof-19 ¶
    - proves proof ch:15-fourier-integral-transforms@proof-7 ¶
  - proves proof ch:15-fourier-integral-transforms@proof-30 ¶
- proves proof ch:15-fourier-integral-transforms@proof-31 ¶
depends_on definition 17.1 Fourier coefficients and Fourier series ¶ ↺

Supports

depends_on proposition 17.26 The lattice harmonics are an orthonormal basis ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Lattice sums and the reciprocal lattice	declared	parts/02-mathematical-methods/15-fourier-integral-transforms.tex:1012
`depends_on`	→	Fourier coefficients and Fourier series	declared	parts/02-mathematical-methods/15-fourier-integral-transforms.tex:1012
`depends_on`	←	The lattice harmonics are an orthonormal basis	declared	parts/02-mathematical-methods/15-fourier-integral-transforms.tex:1031