In this paper we prove a product formula for the c-function associated to a non-compactly causal symmetric space M. Let us recall here the basic facts. Let G be a connected semisimple Lie group, τ:G → G be a non-trivial involution and H = G~τ. Then M := G/H is a semsimple symmetric space. The space M is called non-compactly causal, if q:= {X ∈ g:τ(X) = -X} contains an open H-invariant hyperbolic regular cone C ≠ φ. In this case S := H exp(C) is a open semigroup of G. A spherical function on M is an H-biinvariant continuous function on S/H is contained in M, which defines an eigendistribution of the algebra of H-invariant differential operators on M, see [FHO94], [KNO01], [O197]. There exists a maximal abelian hyperbolic subspace a of q such that C = Ad(H).
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机译：在本文中，我们证明了与非紧致因果对称空间M相关的c函数的乘积公式。在这里让我们回顾一下基本事实。令G为连通的半简单李群，τ：G→G为非平凡对合，且H = G〜τ。那么M：= G / H是一个单纯对称空间。如果q：= {X∈g：τ（X）= -X}包含一个开放的H不变双曲正则圆锥C≠φ，则空间M被称为非紧因果。在这种情况下，S：= H exp（C）是G的一个开放半群。M上的球面函数是S / H上的H双不变连续函数，它定义了H不变代数的本征分布M上的微分运算符，请参见[FHO94]，[KNO01]，[O197]。存在q的最大阿贝尔双曲子空间a，使得C = Ad（H）。
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