List of harmonic analysis and representation theory topics

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.

Fourier analysis

Fourier series

• Periodic function
• Trigonometric function
• Trigonometric polynomial
  • Trigonometric rational function
  • 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

• Linear representation
  • Unitary representation
• Permutation representation
  • Affine representation
  • Projective representation
    • Central extension
• Trivial representation
• Irreducible representation
  • Semisimple
• Group representation
  • Group ring
• Maschke's theorem
• Regular representation
• Character (mathematics)
• Character theory
• Class function
• Representation theory of a finite group
  • Modular representation theory
• 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
  • Universal enveloping algebra
• 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

Applications

• FFT multiplication
• Spectral method
• Fourier transform spectroscopy
• Signal analysis
• Analytic signal
• Welch method