# 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 analysis[edit]

### Fourier series[edit]

- Periodic function
- Trigonometric function
- Trigonometric polynomial
- Dirichlet kernel
- Fejér kernel
- Gibbs phenomenon
- Parseval's identity
- Parseval's theorem
- Weyl differintegral
- Generalized Fourier series
- Set of uniqueness

### Fourier transform[edit]

- 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[edit]

- Topological abelian group
- Haar measure
- Discrete Fourier transform
- Amenable group
- Pontryagin duality
- Kronecker's theorem on diophantine approximation
- Almost periodic function
- Bohr compactification
- Wiener's tauberian theorem

## Representation theory[edit]

- 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[edit]

- Bluestein's FFT algorithm
- Cooley–Tukey FFT algorithm
- Rader's FFT algorithm
- Number-theoretic transform
- Irrational base discrete weighted transform