theorem 17.43 Bandwidth theorem
open in the book ·
parts/02-mathematical-methods/15-fourier-integral-transforms.tex:1701
· p. 691
Rests on
- depends_on equation 17.42 eq:ft-gaussian ¶
-
depends_on
proposition 17.30
Elementary properties
¶
- depends_on definition 17.29 Fourier transform; the treatise convention ¶
- depends_on equation 7.28 eq:ana-parts ¶
-
depends_on
lemma 17.7
Riemann–Lebesgue
¶
-
depends_on
definition 7.39
Darboux sums and the definite integral
¶
- depends_on axiom 7.1 Completeness of $\R$ ¶
- proves proof ch:15-fourier-integral-transforms@proof-5 ¶
-
depends_on
definition 7.39
Darboux sums and the definite integral
¶
- proves proof ch:15-fourier-integral-transforms@proof-19 ¶
-
depends_on
theorem 17.36
Plancherel
¶
- 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 ¶
- proves proof ch:15-fourier-integral-transforms@proof-28 ¶
Supports
- 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 |
|---|---|---|---|---|
depends_on |
→ | eq:ft-gaussian | declared | parts/02-mathematical-methods/15-fourier-integral-transforms.tex:1718 |
depends_on |
→ | Elementary properties | declared | parts/02-mathematical-methods/15-fourier-integral-transforms.tex:1718 |
depends_on |
→ | Plancherel | declared | parts/02-mathematical-methods/15-fourier-integral-transforms.tex:1718 |
depends_on |
← | Duration and bandwidth in SI | declared | parts/02-mathematical-methods/15-fourier-integral-transforms.tex:1770 |
depends_on |
← | The quantum reading, in SI | declared | parts/02-mathematical-methods/15-fourier-integral-transforms.tex:1831 |
proves |
← | ch:15-fourier-integral-transforms@proof-28 | declared | parts/02-mathematical-methods/15-fourier-integral-transforms.tex:1721 |