proposition 17.90 Hankel transform as the axially symmetric Fourier transform

Rests on

• depends_on definition 17.29 Fourier transform; the treatise convention ¶
• depends_on proposition 17.41 The identities physics uses ¶
  • 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 theorem 7.43 Fundamental theorem of calculus, II ¶
    • depends_on definition 7.41 Antiderivative ¶
      • depends_on corollary 7.36 cor:ana-mvt-consequences ¶
        • depends_on theorem 7.35 Mean value theorem ¶
        • proves proof ch:05-real-analysis@proof-20 ¶
      • depends_on definition 7.26 Derivative of a function at a point ¶
        • depends_on definition 7.16 Limit ¶
        • depends_on definition 7.9 Real function ¶
    • depends_on theorem 7.42 Fundamental theorem of calculus, I ¶
      • depends_on definition 7.26 Derivative of a function at a point ¶ ↺
      • depends_on theorem 7.40 Continuous functions are integrable ¶
        • depends_on definition 7.39 Darboux sums and the definite integral ¶
        • depends_on theorem 7.24 Extreme value theorem ¶
        • depends_on theorem 7.25 Heine–Cantor: uniform continuity ¶
        • proves proof ch:05-real-analysis@proof-23 ¶
      • depends_on theorem 7.24 Extreme value theorem ¶ ↺
      • proves proof ch:05-real-analysis@proof-24 ¶
    • proves proof ch:05-real-analysis@proof-25 ¶
  • depends_on theorem 17.32 Fourier inversion ¶ ↺
  • proves proof ch:15-fourier-integral-transforms@proof-26 ¶
• proves proof ch:15-fourier-integral-transforms@proof-55 ¶

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