equation 7.28 eq:ana-parts

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Supports

• depends_on lemma A.193 A cosine integral ¶
  • depends_on lemma A.194 The Fejér kernel and its transform ¶
    • depends_on theorem A.198 Esseen's smoothing inequality ¶
• depends_on lemma A.172 Dirichlet ¶
  • depends_on lemma A.193 A cosine integral ¶ ↺
  • depends_on theorem A.177 Fourier inversion for a distribution function ¶
    • depends_on corollary A.178 The characteristic function determines the distribution ¶
      • depends_on lemma A.220 At each point, field and derivative are independent Gaussians ¶
    • depends_on lemma A.196 Inversion for a difference ¶
      • depends_on theorem A.198 Esseen's smoothing inequality ¶ ↺
• depends_on proposition 17.10 Smoothness and coefficient decay ¶
  • depends_on corollary 17.11 Uniform convergence for $C^{1}$ functions ¶
• depends_on proposition 17.73 Initial- and final-value theorems ¶
• depends_on proposition 17.74 Derivative rule ¶
• depends_on proposition 17.30 Elementary properties ¶
  • depends_on example 17.31 The three standard pairs ¶
  • depends_on proposition 17.39 The transform preserves $\mathcal{S}$ ¶
    • depends_on definition 17.40 Transform and derivative of a distribution ¶
      • depends_on definition 10.42 Green's function ¶
        • depends_on definition 10.50 Retarded and advanced Green's functions ¶
        • depends_on example 10.49 The method of images ¶
        • depends_on proposition 28.24 Impulse response of the damped oscillator ¶
        • depends_on proposition 10.47 Bilinear expansion ¶
        • depends_on proposition 10.43 Representation of the solution ¶
        • depends_on theorem 10.45 Symmetry of the Green's function ¶
      • depends_on proposition 17.41 The identities physics uses ¶
        • depends_on proposition 17.90 Hankel transform as the axially symmetric Fourier transform ¶
        • depends_on proposition 17.52 Linear translation-invariant systems ¶
  • 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 ¶
• depends_on proposition 10.84 Consistency ¶
• depends_on theorem 17.66 Half-plane of convergence ¶