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Journal of Lie Theory 13 (2003), No. 1, 247--261
Copyright Heldermann Verlag 2003

The Product Formula for the Spherical Functions on Symmetric Spaces of Noncompact Type

Piotr Graczyk
Dép. de Mathématiques, Université d'Angers, 49045 Angers, France

Patrice Sawyer
Dept. of Mathematics and Computer Science, Laurentian University, Sudbury, Ontario, Canada P3E 5C6

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.

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