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Harish-Chandra's Ξ function : ウィキペディア英語版
Harish-Chandra's Ξ function
In mathematical harmonic analysis, Harish-Chandra's ''Ξ'' function is a special spherical function on a semisimple Lie group, studied by .
Harish-Chandra used it to define Harish-Chandra's Schwartz space.
gives a detailed description of the properties of ''Ξ''.
==Definition==

:\Xi(g)=\int_Ka(kg)^\rho dk,
where
*''K'' is a maximal compact subgroup of a semisimple Lie group with Iwasawa decomposition ''G''=''NAK''
*''g'' is an element of ''G''
*''ρ'' is a Weyl vector
*''a''(''g'') is the element ''a'' in the Iwasawa decomposition ''g''=''nak''

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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