List of harmonic analysis topics

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.

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

Analysis of unevenly spaced data

 * Least-squares spectral analysis

Applications

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