proposition 17.68 The Laplace transform is a Fourier transform

open in the book · parts/02-mathematical-methods/15-fourier-integral-transforms.tex:2468 · p. 699

Rests on

depends_on definition 17.65 One-sided Laplace transform ¶
depends_on definition 17.29 Fourier transform; the treatise convention ¶
proves proof ch:15-fourier-integral-transforms@proof-41 ¶

Supports

depends_on theorem 17.69 Bromwich inversion integral ¶
- depends_on corollary 17.71 Residue evaluation and causality ¶
  - depends_on corollary 17.76 Heaviside's expansion theorem ¶
  - depends_on proposition 17.77 Poles and stability ¶

Neighborhood

Every logical edge within two steps of this node.

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partly declared
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Edges

type	direction	node	provenance	where
`depends_on`	→	One-sided Laplace transform	declared	parts/02-mathematical-methods/15-fourier-integral-transforms.tex:2475
`depends_on`	→	Fourier transform; the treatise convention	declared	parts/02-mathematical-methods/15-fourier-integral-transforms.tex:2475
`depends_on`	←	Bromwich inversion integral	declared	parts/02-mathematical-methods/15-fourier-integral-transforms.tex:2502
`proves`	←	ch:15-fourier-integral-transforms@proof-41	declared	parts/02-mathematical-methods/15-fourier-integral-transforms.tex:2478