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List of harmonic analysis topics

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This is a list of harmonic analysis topics. See also list of Fourier analysis topics and list of Fourier-related transforms, which are more directed towards the classical Fourier series and Fourier transform of mathematical analysis, mathematical physics and engineering.

Contents

Fourier series

  • Periodic function
  • Trigonometric function
  • Trigonometric polynomial
  • Exponential sum
  • Dirichlet kernel
  • Fejér kernel
  • Gibbs phenomenon
  • Parseval's identity
  • Parseval's theorem
  • Weyl differintegral
  • Generalized Fourier series
  • Orthogonal functions
  • Orthogonal polynomials
  • Empirical orthogonal functions
  • Set of uniqueness

    • Fourier transform

  • Continuous Fourier transform
  • Fourier inversion theorem
  • Plancherel's theorem
  • Convolution
  • Convolution theorem
  • Positive-definite function
  • Poisson summation formula
  • Paley-Wiener theorem
  • Sobolev space
  • Time–frequency representation
  • Quantum Fourier transform

    • Topological groups

  • Topological abelian group
  • Haar measure
  • Discrete Fourier transform
  • Dirichlet character
  • Amenable group
  • Von Neumann's conjecture
  • Pontryagin duality
  • Kronecker's theorem on diophantine approximation
  • Almost periodic function
  • Bohr compactification
  • Wiener's tauberian theorem

    • Representation theory

  • Representation of a Lie group
  • Unitary representation
  • Irreducible representation
  • Harish-Chandra character
  • Restricted representation
  • Induced representation
  • Peter–Weyl theorem
  • Spherical harmonic
  • Casimir operator
  • Hecke operator
  • Stone–von Neumann theorem
  • Discrete series representation
  • Tempered representation
  • Langlands program

    • Fast Fourier transform

  • Bluestein's FFT algorithm
  • Cooley–Tukey FFT algorithm
  • Rader's FFT algorithm
  • Number-theoretic transform
  • Irrational base discrete weighted transform

    • Applications

  • FFT multiplication
  • Spectral method
  • Fourier transform spectroscopy
  • Signal analysis
  • Analytic signal
  • Welch method

    • References

    List of harmonic analysis topics Wikipedia
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