lemma 17.15 A polynomial whose partial sum spikes at the origin

open in the book · parts/02-mathematical-methods/15-fourier-integral-transforms.tex:641 · p. 679

Rests on

depends_on definition 17.1 Fourier coefficients and Fourier series ¶
depends_on lemma 17.14 Uniformly bounded sine sums ¶
- depends_on proposition 8.4 Euler's formula ¶
  - depends_on equation 8.2 eq:cpx-exp-series ¶
  - depends_on proposition 7.47 Comparison; absolute convergence ¶
    - depends_on corollary A.46 Monotone convergence ¶
      - depends_on theorem A.40 Least-upper-bound property ¶
      - proves proof app:A-long-proofs@proof-33 ¶
    - depends_on definition 7.45 Series ¶
      - depends_on definition 7.2 Absolute value ¶
      - depends_on definition 7.4 Convergence ¶
    - depends_on theorem 7.8 Cauchy criterion ¶
      - depends_on corollary A.47 Cauchy completeness ¶
      - depends_on definition 7.4 Convergence ¶ ↺
      - proves proof ch:05-real-analysis@proof-5 ¶
    - proves proof ch:05-real-analysis@proof-28 ¶
  - proves proof ch:06-complex-analysis@proof-2 ¶
- proves proof ch:15-fourier-integral-transforms@proof-12 ¶
proves proof ch:15-fourier-integral-transforms@proof-13 ¶

Supports

depends_on proposition 17.16 An explicit continuous function with a divergent Fourier series ¶

Neighborhood

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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:658
`depends_on`	→	Uniformly bounded sine sums	declared	parts/02-mathematical-methods/15-fourier-integral-transforms.tex:658
`depends_on`	←	An explicit continuous function with a divergent Fourier series	declared	parts/02-mathematical-methods/15-fourier-integral-transforms.tex:702
`proves`	←	ch:15-fourier-integral-transforms@proof-13	declared	parts/02-mathematical-methods/15-fourier-integral-transforms.tex:661