remark 28.26 Causality is visible in the susceptibility

Rests on

• depends_on equation 28.27 eq:osc-susceptibility ¶
• depends_on theorem 17.78 Causality implies dispersion relations ¶
  • depends_on definition 17.29 Fourier transform; the treatise convention ¶
  • depends_on equation 8.16 eq:cpx-simple-pole ¶
  • depends_on lemma 8.9 ML estimate ¶
    • depends_on equation 8.6 eq:cpx-contour-integral ¶
    • proves proof ch:06-complex-analysis@proof-4 ¶
  • depends_on proposition 17.67 Holomorphy ¶
    • depends_on definition 8.5 Complex derivative ¶
    • depends_on definition 17.65 One-sided Laplace transform ¶
    • depends_on theorem 7.38 Taylor's theorem with Lagrange remainder ¶
      • depends_on proposition 7.30 Leibniz rule ¶
        • depends_on definition 7.12 Product of functions ¶
        • depends_on equation 7.14 eq:ana-derivh ¶
        • depends_on proposition 7.27 Differentiable implies continuous ¶
        • depends_on proposition 7.6 Algebra of limits ¶
        • proves proof ch:05-real-analysis@proof-14 ¶
      • depends_on theorem 7.34 Rolle ¶
        • depends_on lemma 7.33 Fermat: interior extremum ¶
        • depends_on theorem 7.24 Extreme value theorem ¶
        • proves proof ch:05-real-analysis@proof-18 ¶
      • proves proof ch:05-real-analysis@proof-22 ¶
    • proves proof ch:15-fourier-integral-transforms@proof-40 ¶
  • depends_on proposition 17.42 Sokhotski–Plemelj ¶
    • 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 ¶
  • depends_on theorem 8.12 Cauchy ¶
    • depends_on equation 8.5 eq:cpx-cr ¶
    • depends_on theorem 7.131 Green ¶
      • depends_on definition 7.127 Simple regions ¶
        • depends_on definition 7.98 Functions of class $C^{1}$ ¶
        • depends_on definition 6.9 Compact set ¶
      • depends_on remark 7.128 What the derivations below take as given ¶
        • depends_on definition 7.125 Multiple integral ¶
        • depends_on theorem 7.40 Continuous functions are integrable ¶
        • depends_on theorem 7.25 Heine–Cantor: uniform continuity ¶
      • depends_on theorem 7.43 Fundamental theorem of calculus, II ¶
        • depends_on definition 7.41 Antiderivative ¶
        • depends_on theorem 7.42 Fundamental theorem of calculus, I ¶
        • proves proof ch:05-real-analysis@proof-25 ¶
      • proves proof ch:05-real-analysis@proof-77 ¶
    • proves proof ch:06-complex-analysis@proof-7 ¶
  • proves proof ch:15-fourier-integral-transforms@proof-49 ¶

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