theorem 17.36 Plancherel
open in the book ·
parts/02-mathematical-methods/15-fourier-integral-transforms.tex:1435
· p. 688
Rests on
- depends_on definition 17.29 Fourier transform; the treatise convention ¶
-
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-24 ¶
Supports
-
depends_on
theorem 17.43
Bandwidth theorem
¶
- depends_on corollary 17.44 Duration and bandwidth in SI ¶
- depends_on remark 17.46 The quantum reading, in SI ¶
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 |
|---|---|---|---|---|
cites |
→ | Contribution À ĽÉtude de la reprÉsentation D'une fonction arbitraire par des intÉgrales dÉfinies | derived | parts/02-mathematical-methods/15-fourier-integral-transforms.tex:1446 |
depends_on |
→ | Fourier transform; the treatise convention | declared | parts/02-mathematical-methods/15-fourier-integral-transforms.tex:1447 |
depends_on |
→ | Fourier inversion | declared | parts/02-mathematical-methods/15-fourier-integral-transforms.tex:1447 |
depends_on |
← | Bandwidth theorem | declared | parts/02-mathematical-methods/15-fourier-integral-transforms.tex:1718 |
proves |
← | ch:15-fourier-integral-transforms@proof-24 | declared | parts/02-mathematical-methods/15-fourier-integral-transforms.tex:1450 |