Geodesic
A Sharp Criterion for the Existence of the Density in the Product Formula on Symmetric Spaces of Type An
Piotr Graczyk1 ; Patrice Sawyer2
1Dép. de Mathématiques, Université d'Angers, 2 Boulevard Lavoisier, 49045 Angers, France
2Dept. of Mathematics and Computer Science, Laurentian University, Sudbury, Ontario, Canada P3E 5C6
Journal of Lie Theory, Tome 20 (2010) no. 4, pp. 751-766

Voir la notice de l'article provenant de la source Heldermann Verlag

\def\a{{\frak a}} \def\C{{\Bbb C}} \def\F{{\Bbb F}} \def\H{{\Bbb H}} \def\R{{\Bbb R}} We find sharp conditions on $X,Y\in\a$ for the existence of the density of the measure $\delta_{e^X}^\natural \star \delta_{e^Y}^\natural$ intervening in the product formula for the spherical functions on the symmetric spaces of noncompact type ${\bf X}={\bf SL}(n,\F)/{\bf SU}(n,\F)$ where $\F=\R$, $\C$ or $\H$. Our results also apply to the symmetric space ${\bf E}_6/{\bf F}_4$.
Classification : 43A90, 53C35, 15A18
Mots-clés : Product formula, convolution of measures, semisimple Lie groups

Piotr Graczyk  1   ; Patrice Sawyer  2

1 Dép. de Mathématiques, Université d'Angers, 2 Boulevard Lavoisier, 49045 Angers, France
2 Dept. of Mathematics and Computer Science, Laurentian University, Sudbury, Ontario, Canada P3E 5C6 
Piotr Graczyk; Patrice Sawyer. A Sharp Criterion for the Existence of the Density in the Product Formula on Symmetric Spaces of Type An. Journal of Lie Theory, Tome 20 (2010) no. 4, pp. 751-766. http://geodesic.mathdoc.fr/item/JOLT_2010_20_4_a7/
@article{JOLT_2010_20_4_a7,
     author = {Piotr Graczyk and Patrice Sawyer},
     title = {A {Sharp} {Criterion} for the {Existence} of the {Density} in the {Product} {Formula} on {Symmetric} {Spaces} of {Type} {A\protect\textsubscript{n}}},
     journal = {Journal of Lie Theory},
     pages = {751--766},
     year = {2010},
     volume = {20},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2010_20_4_a7/}
}
TY  - JOUR
AU  - Piotr Graczyk
AU  - Patrice Sawyer
TI  - A Sharp Criterion for the Existence of the Density in the Product Formula on Symmetric Spaces of Type An
JO  - Journal of Lie Theory
PY  - 2010
SP  - 751
EP  - 766
VL  - 20
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/JOLT_2010_20_4_a7/
ID  - JOLT_2010_20_4_a7
ER  - 
%0 Journal Article
%A Piotr Graczyk
%A Patrice Sawyer
%T A Sharp Criterion for the Existence of the Density in the Product Formula on Symmetric Spaces of Type An
%J Journal of Lie Theory
%D 2010
%P 751-766
%V 20
%N 4
%U http://geodesic.mathdoc.fr/item/JOLT_2010_20_4_a7/
%F JOLT_2010_20_4_a7