Abstract :
[en] We give an integral representation of $K$-positive definite functions on a real rank $n$ connected, noncompact, semisimple Lie group with finite centre. Moreover, we characterize the $\lambda$'s for which the $\tau$-spherical function $\phi_{\sigma,\lambda}^\tau$ is positive definite for the group $G=\mathrm{Spin}_e(n,1)$ and the complex spin representation $\tau$.
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