Fourier analysis on LCA

  • Pontryagin duality
  • compactness-discreteness duality
  • time-frequency considerations
  • Haar measure
  • Bochner-Khinchin theorem, etc.
  • Fourier inversion theorem
  • Plencherel theorem
  • decay-smoothness duality
  • Paley-Wiener-Schwartz theorem
  • uncertainty principle
  • maximal ideals of L^{1}(G)
  • Banach-algebra considerations
  • Reference: Walter Rudin, Fourier analysis on groups.

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