proposition 10.63 Infinite propagation speed

open in the book · parts/02-mathematical-methods/08-pdes.tex:1735 · p. 358

Rests on

depends_on theorem 10.62 The heat kernel ¶
- depends_on equation 17.42 eq:ft-gaussian ¶
- depends_on proposition 10.39 Fourier reduction on the line ¶
  - depends_on definition 17.29 Fourier transform; the treatise convention ¶
  - depends_on equation 17.38 eq:ft-derivative ¶
  - proves proof ch:08-pdes@proof-12 ¶
- depends_on theorem 17.53 Convolution theorem ¶
  - depends_on definition 17.50 Convolution ¶
  - depends_on definition 17.29 Fourier transform; the treatise convention ¶ ↺
  - depends_on proposition 17.51 Algebra of convolution ¶
    - depends_on definition 17.50 Convolution ¶ ↺
    - proves proof ch:15-fourier-integral-transforms@proof-32 ¶
  - depends_on theorem 17.32 Fourier inversion ¶
    - depends_on definition 17.29 Fourier transform; the treatise convention ¶ ↺
    - depends_on equation 17.42 eq:ft-gaussian ¶ ↺
    - proves proof ch:15-fourier-integral-transforms@proof-20 ¶
  - proves proof ch:15-fourier-integral-transforms@proof-34 ¶
- proves proof ch:08-pdes@proof-25 ¶
proves proof ch:08-pdes@proof-26 ¶

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type	direction	node	provenance	where
`depends_on`	→	The heat kernel	declared	parts/02-mathematical-methods/08-pdes.tex:1741
`proves`	←	ch:08-pdes@proof-26	declared	parts/02-mathematical-methods/08-pdes.tex:1744