List of Fourier analysis topics

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

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
• Entropy influence conjecture
• Fast cosine transform
• Fast Fourier transform
• Cyclotomic fast Fourier transform
• Sparse 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

Integral transform concepts

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