definition 10.50 Retarded and advanced Green's functions

Rests on

• depends_on definition 10.42 Green's function ¶
  • depends_on definition 17.40 Transform and derivative of a distribution ¶
    • depends_on definition 17.38 Schwartz space and tempered distributions ¶
    • depends_on proposition 17.39 The transform preserves $\mathcal{S}$ ¶
      • depends_on definition 17.38 Schwartz space and tempered distributions ¶ ↺
      • 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 ¶
        • proves proof ch:15-fourier-integral-transforms@proof-19 ¶
      • 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-25 ¶
  • depends_on definition 10.4 The second-order operator ¶
    • depends_on definition 10.3 Principal part and principal symbol ¶
      • depends_on definition 10.2 Linear, semilinear, quasilinear ¶
        • depends_on definition 10.1 Partial differential equation; order ¶
      • depends_on equation 10.2 eq:pde-multi-index ¶
    • depends_on proposition 7.105 Clairaut–Schwarz ¶
      • depends_on definition 7.20 Continuity at a point ¶
        • depends_on definition 7.16 Limit ¶
        • depends_on equation 7.7 eq:ana-limit-left ¶
        • depends_on equation 7.5 eq:ana-limit-right ¶
      • depends_on theorem 7.35 Mean value theorem ¶
        • depends_on proposition 7.29 Linearity ¶
        • depends_on theorem 7.34 Rolle ¶
        • proves proof ch:05-real-analysis@proof-19 ¶
      • proves proof ch:05-real-analysis@proof-64 ¶
• depends_on equation 10.1 eq:pde-dalembertian ¶

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