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About: Plancherel theorem for spherical functions     Goto   Sponge   NotDistinct   Permalink

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Type: Thingyago:WikicatTheoremsInFunctionalAnalysisyago:WikicatTheoremsInHarmonicAnalysisyago:Abstraction100002137yago:Communication100033020yago:Message106598915yago:Proposition106750804yago:Statement106722453yago:Theorem106752293 New Facet based on Instances of this Class

In mathematics, the Plancherel theorem for spherical functions is an important result in the representation theory of semisimple Lie groups, due in its final form to Harish-Chandra. It is a natural generalisation in non-commutative harmonic analysis of the Plancherel formula and Fourier inversion formula in the representation theory of the group of real numbers in classical harmonic analysis and has a similarly close interconnection with the theory of differential equations.It is the special case for zonal spherical functions of the general Plancherel theorem for semisimple Lie groups, also proved by Harish-Chandra. The Plancherel theorem gives the eigenfunction expansion of radial functions for the Laplacian operator on the associated symmetric space X; it also gives the direct integral d