In mathematics, specifically harmonic analysis, Harish-Chandra's Ξ function is a special spherical function on a semisimple Lie group. It was introduced by Harish-Chandra, who used it to define his Schwartz space.
For a maximal compact subgroup of a semisimple Lie group with Iwasawa decomposition , an element of , the element in the Iwasawa decomposition and a Weyl vector, the function is defined as
.
Wallach gives a detailed description of the properties of .
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