This is a list of Fourier analysis topics. See also the list of Fourier-related transforms, and the list of harmonic analysis topics.
Fourier analysis edit
Fourier series edit
- Generalized Fourier series
- Regressive discrete Fourier series
- Gibbs phenomenon
- Sigma approximation
- Dini test
- Poisson summation formula
- Spectrum continuation analysis
- Convergence of Fourier series
Fourier transforms edit
- List of Fourier-related transforms
- Fourier transform on finite groups
- Fractional Fourier transform
- Continuous Fourier transform
- Fourier operator
- Fourier inversion theorem
- Sine and cosine transforms
- Parseval's theorem
- Paley–Wiener theorem
- Projection-slice theorem
- Frequency spectrum
Discrete Fourier transforms edit
- Discrete Fourier series
- Non-uniform discrete Fourier transform
- DFT matrix
- Entropy influence conjecture
- Fast cosine transform
- Fast Fourier transform
- Cyclotomic fast Fourier transform
- Sparse Fourier transform
Applications of Fourier analysis edit
Algebra and analysis edit
- Periodic function
- Almost periodic function
- ATS theorem
- Modulus of continuity
- Banach algebra
- Compact group
- Haar measure
- Hardy space
- Sobolev space
- Topological group
Harmonic analysis edit
- Set of uniqueness
- Pontryagin duality
- Plancherel theorem
- Peter–Weyl theorem
- Fourier integral operator
- Oscillatory integral operator