View source for List of Fourier analysis topics

{{Short description|none}}
This is a '''list of [[Fourier analysis]] topics'''. See also the [[List of Fourier-related transforms|list of Fourier-related transforms]], and the [[List of harmonic analysis topics|list of harmonic analysis topics]].

==[[Fourier analysis]]==

* [[Multiplier (Fourier analysis)]]
* [[Fourier shell correlation]]
* [[Pinsky phenomenon]]

===[[Fourier series]]===

* [[Generalized Fourier series]]
* [[Regressive discrete Fourier series]]
* [[Gibbs phenomenon]]
* [[Sigma approximation]]
* [[Dini test]]
* [[Poisson summation formula]]
* [[Spectrum continuation analysis]]
* [[Convergence of Fourier series]]

===[[Fourier transform]]s===

* [[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]]
* [[Physics:Frequency spectrum|Frequency spectrum]]

===[[Discrete Fourier transform]]s===

* [[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===

* [[Fourier amplitude sensitivity testing]]
* [[Fourier optics]]
* [[Physics:Quantum mechanics|Quantum mechanics]], for 
**Wavefunctions
**[[Physics:Uncertainty principle|Uncertainty principle]]
**[[Quantum Fourier transform]]

==[[Algebra]] and [[Mathematical analysis|analysis]]==

* [[Periodic function]]
* [[Almost periodic function]]
* [[ATS theorem]]
* [[Modulus of continuity]]
* [[Banach algebra]]
* [[Compact group]]
* [[Haar measure]]
* [[Hardy space]]
* [[Sobolev space]]
* [[Topological group]]

===[[Physics:Harmonic analysis|Harmonic analysis]]===

* [[Set of uniqueness]]
* [[Pontryagin duality]]
* [[Plancherel theorem]]
* [[Peter–Weyl theorem]]
* [[Fourier integral operator]]
* [[Oscillatory integral operator]]

===[[Harmonic function]]s===

* [[Laplace operator]]
* Laplace equation
* [[Dirichlet problem]]
* [[Unit circle]]
* Unit disc
* [[Physics:Spherical harmonic|Spherical harmonic]]

===[[Special functions]] and [[Generalized function|generalized function]]s===

* [[Bessel function]]
* [[Dirac delta function]]
* [[Distribution (mathematics)|Distribution]]
* [[Oscillatory integral]]

==[[Integral transform]] concepts==

===Transforms===

* [[Laplace transform]]
* [[Discrete Hartley transform]]
* [[List of transforms]]

===Integral kernels===

* [[Dirichlet kernel]]
* [[Fejér kernel]]

===[[Convolution]]===

* [[Convolution theorem]]

==Analysis of unevenly spaced data==

* [[Least-squares spectral analysis]]

==Other topics==

* [[List of cycles]]
* LTI system theory
* [[Autocorrelation]]
* [[Autocovariance]]
* [[Whittaker–Shannon interpolation formula]]
* [[Gabor atom]]
* Marcinkiewicz theorem
* [[Nyquist–Shannon sampling theorem]]
* [[Riesz–Thorin theorem]]

[[Category:Mathematics-related lists|Fourier analysis]]
[[Category:Fourier analysis| ]]
[[Category:Outlines of mathematics and logic|Fourier analysis]]
[[Category:Outlines|Fourier analysis]]

{{Sourceattribution|List of Fourier analysis topics}}