definition 8.5 Complex derivative

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Supports

• depends_on proposition 17.67 Holomorphy ¶
  • 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 ¶
  • depends_on theorem 17.93 Fundamental strip and holomorphy ¶
    • depends_on theorem 17.94 Mellin inversion ¶
      • depends_on proposition 17.96 Poles give asymptotics ¶
      • depends_on theorem 17.100 Moments diagonalise a convolution evolution ¶
        • depends_on corollary 17.101 Coupled channels ¶
• depends_on proposition 12.53 The resolvent set is open, the resolvent analytic ¶
  • depends_on theorem 12.54 The spectrum is compact and non-empty ¶
    • depends_on theorem 12.55 The spectrum of a self-adjoint operator is real ¶
      • depends_on example 12.56 Multiplication by the coordinate: spectrum without eigenvectors ¶
      • depends_on theorem A.238 Spectral theorem, both forms ¶
        • depends_on proposition A.280 Direct-integral form of the spectral theorem ¶
        • depends_on proposition A.261 Spectral theorem for a unitary operator ¶
        • depends_on theorem A.279 Gelfand–Maurin ¶
        • depends_on theorem A.253 Stone ¶
      • depends_on theorem 12.59 Spectral theorem for a bounded self-adjoint operator ¶
        • depends_on definition 12.60 Functional calculus ¶
        • depends_on theorem 12.107 Nuclear spectral theorem ¶
        • depends_on theorem 12.91 Schur's lemma, commutant form ¶
        • depends_on theorem 12.66 Stone ¶
• depends_on theorem A.783 Riemann mapping with boundary correspondence, quoted ¶
  • depends_on corollary A.788 The two parameters are the same parameter ¶
    • depends_on theorem A.789 Kirchhoff's contraction coefficient ¶