Supriya Ghosh (Editor)

List of Fourier analysis topics

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This is a list of Fourier analysis topics. See also the list of Fourier-related transforms, and the list of harmonic analysis topics.

Contents

Fourier analysis

  • Multiplier (Fourier analysis)
  • Fourier shell correlation
  • Pinsky phenomenon

    • Fourier series

  • Generalized Fourier series
  • Regressive discrete Fourier series
  • Gibbs phenomenon
  • Sigma approximation
  • Dini test
  • Poisson summation formula
  • Spectrum continuation analysis
  • Convergence of Fourier series

    • Fourier transforms

  • List of Fourier-related transforms
  • Fourier transform on finite groups
  • Fractional Fourier transform
  • Continuous Fourier transform
  • Fourier operator
  • Fourier inversion theorem
  • Sine and cosine transforms
  • Parseval's theorem
  • Paley–Wiener theorem
  • Projection-slice theorem
  • Frequency spectrum

    • Discrete Fourier transforms

  • Discrete Fourier series
  • Non-uniform discrete Fourier transform
  • DFT matrix
  • Fast cosine transform
  • Fast Fourier transform
  • Cyclotomic fast Fourier transform

    • Applications of Fourier analysis

  • Fourier amplitude sensitivity testing
  • Fourier optics
  • Quantum mechanics, for
  • Wavefunctions
  • Uncertainty principle
  • Quantum Fourier transform

    • Algebra and analysis

  • Periodic function
  • Almost periodic function
  • ATS theorem
  • Modulus of continuity
  • Banach algebra
  • Compact group
  • Haar measure
  • Hardy space
  • Sobolev space
  • Topological group

    • Harmonic analysis

  • Set of uniqueness
  • Pontryagin duality
  • Plancherel theorem
  • Peter–Weyl theorem
  • Fourier integral operator
  • Oscillatory integral operator

    • Harmonic functions

  • Laplace operator
  • Laplace equation
  • Dirichlet problem
  • Unit circle
  • Unit disc
  • Spherical harmonic

    • Special functions and generalized functions

  • Bessel function
  • Dirac delta function
  • Distribution
  • Oscillatory integral

    • Transforms

  • Laplace transform
  • Discrete Hartley transform
  • List of transforms

    • Integral kernels

  • Dirichlet kernel
  • Fejér kernel

    • Convolution

  • Convolution theorem

    • Other topics

  • List of cycles
  • LTI system theory
  • Autocorrelation
  • Autocovariance
  • Whittaker–Shannon interpolation formula
  • Gabor atom
  • Marcinkiewicz theorem
  • Nyquist–Shannon sampling theorem
  • Riesz–Thorin theorem

    • References

    List of Fourier analysis topics Wikipedia
    (Text) CC BY-SA


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