Geodesic
The Product Formula for the Spherical Functions on Symmetric Spaces of Noncompact Type
Journal of Lie theory, Tome 13 (2003) no. 1, pp. 247-261 Cet article a éte moissonné depuis la source Heldermann Verlag

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We prove the existence of the product formula for the spherical functions on symmetric spaces of noncompact type.  To this end, we study the analyticity properties of the Cartan decomposition and we find a limited Taylor expansion of the abelian factor in this decomposition. 
@article{JLT_2003_13_1_JLT_2003_13_1_a13,
     author = {P. Graczyk and P. Sawyer },
     title = {The {Product} {Formula} for the {Spherical} {Functions} on {Symmetric} {Spaces} of {Noncompact} {Type}},
     journal = {Journal of Lie theory},
     pages = {247--261},
     year = {2003},
     volume = {13},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JLT_2003_13_1_JLT_2003_13_1_a13/}
}
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P. Graczyk; P. Sawyer . The Product Formula for the Spherical Functions on Symmetric Spaces of Noncompact Type. Journal of Lie theory, Tome 13 (2003) no. 1, pp. 247-261. http://geodesic.mathdoc.fr/item/JLT_2003_13_1_JLT_2003_13_1_a13/