Editing 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]].

==[[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 group]]s==

*[[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]]==

{{main|List of representation theory topics}}

*[[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]]

[[Category:Mathematics-related lists|Harmonic analysis]]
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[[Category:Outlines of mathematics and logic|Harmonic analysis]]
[[Category:Outlines|Harmonic analysis]]