e/Noncommutative harmonic analysis

Information
has gloss	eng: In mathematics, noncommutative harmonic analysis is the field in which results from Fourier analysis are extended to topological groups which are not commutative. Since for locally compact abelian groups have a well-understood theory, Pontryagin duality, which includes the basic structures of Fourier series and Fourier transforms, the major business of non-commutative harmonic analysis is usually taken to be the extension of the theory to all groups G that are locally compact. The case of compact groups is understood, qualitatively and after the Peter-Weyl theorem from the 1920s, as being generally analogous to that of finite groups and their character theory.
lexicalization	eng: Non-commutative harmonic analysis
lexicalization	eng: Noncommutative harmonic analysis
instance of	c/Duality theories