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An analogue of Krein’s theorem for semisimple Lie groups

An analogue of Krein’s theorem for semisimple Lie groups

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 λ's for which the τ -spherical function φ τ σ,λ is positive definite for the group G = Spin e (n, 1) and the …