Editing Fourier analysis (section)

==Fourier transforms on arbitrary locally compact abelian topological groups==
The Fourier variants can also be generalized to Fourier transforms on arbitrary [[locally compact]] [[Abelian group|Abelian]] [[topological group]]s, which are studied in [[harmonic analysis]]; there, the Fourier transform takes functions on a group to functions on the dual group. This treatment also allows a general formulation of the [[convolution theorem]], which relates Fourier transforms and [[convolution]]s. See also the [[Pontryagin duality]] for the generalized underpinnings of the Fourier transform.

More specific, Fourier analysis can be done on cosets,<ref name=Forrest/> even discrete cosets.