Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Plancherel_theorem_for_spherical_functions> ?p ?o }
- Plancherel_theorem_for_spherical_functions abstract "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 decomposition into irreducible representations of the regular representation on L2(X). In the case ofhyperbolic space, these expansions were known from prior results of Mehler, Weyl and Fock.The main reference for almost all this material is the encyclopedic text of Helgason (1984).".
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- Plancherel_theorem_for_spherical_functions wikiPageWikiLink C*-algebra.
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- Plancherel_theorem_for_spherical_functions wikiPageWikiLink Category:Representation_theory_of_Lie_groups.
- Plancherel_theorem_for_spherical_functions wikiPageWikiLink Category:Theorems_in_functional_analysis.
- Plancherel_theorem_for_spherical_functions wikiPageWikiLink Category:Theorems_in_harmonic_analysis.
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- Plancherel_theorem_for_spherical_functions wikiPageWikiLink Proceedings_of_the_USSR_Academy_of_Sciences.
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