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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
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
is the element
a
in the
Iwasawa
decomposition
g
=
nak
