proposition 17.42 Sokhotski–Plemelj
open in the book ·
parts/02-mathematical-methods/15-fourier-integral-transforms.tex:1652
· p. 690
Rests on
- depends_on definition 17.38 Schwartz space and tempered distributions ¶
-
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-27 ¶
Supports
-
depends_on
proposition 105.22
The two-state effective generator
¶
- depends_on proposition 105.23 Symmetry constraints on the mass matrix ¶
-
depends_on
theorem 17.78
Causality implies dispersion relations
¶
- depends_on remark 33.10 Fibre anelasticity, and why it biases one method and not the other ¶
- depends_on remark 28.26 Causality is visible in the susceptibility ¶
- depends_on remark 28.62 Neither velocity is a speed limit ¶
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 |
→ | Schwartz space and tempered distributions | declared | parts/02-mathematical-methods/15-fourier-integral-transforms.tex:1661 |
depends_on |
→ | Fourier inversion | declared | parts/02-mathematical-methods/15-fourier-integral-transforms.tex:1661 |
depends_on |
← | The two-state effective generator | declared | parts/11-qft-standard-model/07-discrete-symmetries-cpt.tex:1618 |
depends_on |
← | Causality implies dispersion relations | declared | parts/02-mathematical-methods/15-fourier-integral-transforms.tex:2772 |
proves |
← | ch:15-fourier-integral-transforms@proof-27 | declared | parts/02-mathematical-methods/15-fourier-integral-transforms.tex:1664 |