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- 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).".
- Plancherel_theorem_for_spherical_functions wikiPageID "18298785".
- Plancherel_theorem_for_spherical_functions wikiPageRevisionID "583916847".
- Plancherel_theorem_for_spherical_functions hasPhotoCollection Plancherel_theorem_for_spherical_functions.
- Plancherel_theorem_for_spherical_functions subject Category:Representation_theory_of_Lie_groups.
- Plancherel_theorem_for_spherical_functions subject Category:Theorems_in_functional_analysis.
- Plancherel_theorem_for_spherical_functions subject Category:Theorems_in_harmonic_analysis.
- Plancherel_theorem_for_spherical_functions type Abstraction100002137.
- Plancherel_theorem_for_spherical_functions type Communication100033020.
- Plancherel_theorem_for_spherical_functions type Message106598915.
- Plancherel_theorem_for_spherical_functions type Proposition106750804.
- Plancherel_theorem_for_spherical_functions type Statement106722453.
- Plancherel_theorem_for_spherical_functions type Theorem106752293.
- Plancherel_theorem_for_spherical_functions type TheoremsInFunctionalAnalysis.
- Plancherel_theorem_for_spherical_functions type TheoremsInHarmonicAnalysis.
- Plancherel_theorem_for_spherical_functions comment "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.".
- Plancherel_theorem_for_spherical_functions label "Plancherel theorem for spherical functions".
- Plancherel_theorem_for_spherical_functions label "球函数に対するプランシュレルの定理".
- Plancherel_theorem_for_spherical_functions sameAs 球函数に対するプランシュレルの定理.
- Plancherel_theorem_for_spherical_functions sameAs m.04cvlxw.
- Plancherel_theorem_for_spherical_functions sameAs Q11573495.
- Plancherel_theorem_for_spherical_functions sameAs Q11573495.
- Plancherel_theorem_for_spherical_functions sameAs Plancherel_theorem_for_spherical_functions.
- Plancherel_theorem_for_spherical_functions wasDerivedFrom Plancherel_theorem_for_spherical_functions?oldid=583916847.
- Plancherel_theorem_for_spherical_functions isPrimaryTopicOf Plancherel_theorem_for_spherical_functions.