List of harmonic analysis and representation theory topics
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This is a list of harmonic analysis and representation theory topics, by Wikipedia page. 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.
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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
- Pontryagin duality
- Kronecker's theorem on diophantine approximation
- Almost periodic function
- Bohr compactification
- Wiener's tauberian theorem
Representation theory
- Linear representation
- Permutation representation
- Trivial representation
- Irreducible representation
- Group representation
- Maschke's theorem
- Regular representation
- Character (mathematics)
- Character theory
- Class function
- Representation theory of a finite group
- real representation
- Pseudoreal representation, symplectic representation
- Complex representation
- Schur's lemma
- Restricted representation
- Induced representation
- Peter-Weyl theorem
- Young tableau
- Spherical harmonic
- Casimir operator
- Hecke operator
- Representation theory of the symmetric group
- Representation theory of diffeomorphism groups
- Unitary representations of a star Lie superalgebra
Representations of Lie groups
- Fundamental representation
- Antifundamental representation
- Bifundamental representation
- Adjoint representation
- Root system
- Representation of Lie algebras
- Weight (representation theory)
- Cartan's theorem
- Spinor
- Wigner's classification
- Wigner-Eckart theorem
- Invariant theory
- Stone-von Neumann theorem
- Borel-Bott-Weil theorem
- Representation theory of the Poincaré group
Fast Fourier transform
- Bluestein's FFT algorithm
- Cooley-Tukey FFT algorithm
- Rader's FFT algorithm
- Number-theoretic transform
- Irrational base discrete weighted transform