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 analysis
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