Abstract
We find a characterization of the spherical Fourier transformof K- invariant probability measures on Riemannian symmetric spaces of noncompact type in the complex case. To do this we use some interesting properties of holomorphic functions on an n-dimensional complex linear space connected with functions of positive type and complex Fourier transform. We also characterize the spherical Fourier transform of infinitely divisible measures in the symmetric complex case.
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