definition 17.29 Fourier transform; the treatise convention

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• depends_on corollary 17.49 Lattice sums and the reciprocal lattice ¶
  • depends_on definition 17.25 Multiple Fourier series ¶
    • depends_on proposition 17.26 The lattice harmonics are an orthonormal basis ¶
• depends_on definition 17.79 Band-limited function ¶
  • depends_on corollary 17.81 Sampling periodises the spectrum; aliasing ¶
  • depends_on theorem 17.80 Sampling theorem ¶
    • depends_on corollary 17.107 How many projections ¶
• depends_on definition 17.58 Stationary process and power spectral density ¶
  • depends_on theorem 17.63 Matched filter ¶
  • depends_on theorem 17.59 Wiener–Khinchin ¶
    • depends_on proposition 17.61 Mean-square response of a damped resonator ¶
• depends_on definition 25.52 Wigner function ¶
  • depends_on definition A.605 The analytic continuation of the overlaps ¶
    • depends_on lemma A.606 $F$ is entire, and is the overlap in disguise ¶
      • depends_on lemma A.607 A zero-free entire function is an exponential ¶
        • depends_on proposition A.609 The exponent is a quadratic polynomial ¶
• depends_on example 17.31 The three standard pairs ¶
• depends_on lemma A.584 Fourier injectivity in $n$ variables ¶
  • depends_on theorem A.587 The Gaussian average is a non-zero projector that absorbs the Weyl operators ¶
    • depends_on lemma A.590 The Gram matrix is universal ¶
      • depends_on proposition A.591 Any two irreducible Weyl systems are equivalent ¶
    • depends_on proposition A.589 Cyclic subspaces and the rank of the average ¶
      • depends_on lemma A.590 The Gram matrix is universal ¶ ↺
      • depends_on proposition A.591 Any two irreducible Weyl systems are equivalent ¶ ↺
    • depends_on proposition A.592 The vacuum of the Schrödinger system ¶
• depends_on lemma 17.35 Multiplication formula ¶
• depends_on proposition 17.90 Hankel transform as the axially symmetric Fourier transform ¶
• depends_on proposition 17.68 The Laplace transform is a Fourier transform ¶
  • depends_on theorem 17.69 Bromwich inversion integral ¶
    • depends_on corollary 17.71 Residue evaluation and causality ¶
      • depends_on corollary 17.76 Heaviside's expansion theorem ¶
      • depends_on proposition 17.77 Poles and stability ¶
• 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 28.60 A wave packet translates at $v_{g}$ and spreads at a rate set by the curvature of $\omega(k)$ ¶
• depends_on proposition 10.39 Fourier reduction on the line ¶
  • depends_on theorem 10.62 The heat kernel ¶
    • depends_on proposition 10.63 Infinite propagation speed ¶
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