Spherical functions on ordered symmetric spaces

Jacques Faraut; Joachim Hilgert; Gestur Ólafsson

Annales de l'institut Fourier (1994)

  • Volume: 44, Issue: 3, page 927-965
  • ISSN: 0373-0956

Abstract

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We define on an ordered semi simple symmetric space ℳ = G / H a family of spherical functions by an integral formula similar to the Harish-Chandra integral formula for spherical functions on a Riemannian symmetric space of non compact type. Associated with these spherical functions we define a spherical Laplace transform. This transform carries the composition product of invariant causal kernels onto the ordinary product. We invert this transform when G is a complex group, H a real form of G , and when ℳ is a symmetric space of rank one.

How to cite

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Faraut, Jacques, Hilgert, Joachim, and Ólafsson, Gestur. "Spherical functions on ordered symmetric spaces." Annales de l'institut Fourier 44.3 (1994): 927-965. <http://eudml.org/doc/75085>.

@article{Faraut1994,
abstract = {We define on an ordered semi simple symmetric space $\{\cal M\}=G/H$ a family of spherical functions by an integral formula similar to the Harish-Chandra integral formula for spherical functions on a Riemannian symmetric space of non compact type. Associated with these spherical functions we define a spherical Laplace transform. This transform carries the composition product of invariant causal kernels onto the ordinary product. We invert this transform when $G$ is a complex group, $H$ a real form of $G$, and when $\{\cal M\}$ is a symmetric space of rank one.},
author = {Faraut, Jacques, Hilgert, Joachim, Ólafsson, Gestur},
journal = {Annales de l'institut Fourier},
keywords = {ordered semisimple symmetric space; spherical functions; Harish-Chandra integral formula; Riemannian symmetric space; spherical Laplace transform},
language = {eng},
number = {3},
pages = {927-965},
publisher = {Association des Annales de l'Institut Fourier},
title = {Spherical functions on ordered symmetric spaces},
url = {http://eudml.org/doc/75085},
volume = {44},
year = {1994},
}

TY - JOUR
AU - Faraut, Jacques
AU - Hilgert, Joachim
AU - Ólafsson, Gestur
TI - Spherical functions on ordered symmetric spaces
JO - Annales de l'institut Fourier
PY - 1994
PB - Association des Annales de l'Institut Fourier
VL - 44
IS - 3
SP - 927
EP - 965
AB - We define on an ordered semi simple symmetric space ${\cal M}=G/H$ a family of spherical functions by an integral formula similar to the Harish-Chandra integral formula for spherical functions on a Riemannian symmetric space of non compact type. Associated with these spherical functions we define a spherical Laplace transform. This transform carries the composition product of invariant causal kernels onto the ordinary product. We invert this transform when $G$ is a complex group, $H$ a real form of $G$, and when ${\cal M}$ is a symmetric space of rank one.
LA - eng
KW - ordered semisimple symmetric space; spherical functions; Harish-Chandra integral formula; Riemannian symmetric space; spherical Laplace transform
UR - http://eudml.org/doc/75085
ER -

References

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