Harish-Chandra's Ξ function
Encyclopedia
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.
where
Harish-Chandra used it to define Harish-Chandra's Schwartz space
Harish-Chandra's Schwartz space
In mathematical abstract harmonic analysis, Harish-Chandra's Schwartz space is a space of functions on a semisimple Lie group whose derivatives are rapidly decreasing, studied by...
.
gives a detailed description of the properties of Ξ.
Definition
where
- K is a maximal compact subgroup of a semisimple Lie group with Iwasawa decompositionIwasawa decompositionIn mathematics, the Iwasawa decomposition KAN of a semisimple Lie group generalises the way a square real matrix can be written as a product of an orthogonal matrix and an upper triangular matrix...
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