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
Fourier series
- 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
- 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
- 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
Applications
- FFT multiplication
- Spectral method
- Fourier transform spectroscopy
- Signal analysis
- Analytic signal
- Welch method
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