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A Paley-Wiener theorem for the inverse spherical transform. (English) Zbl 1014.22010
A Paley-Wiener theorem for the inverse spherical transform is proved for noncompact semisimple Lie groups which are either of rank one or have a complex structure. The proof relies on the explicit inversion formula for the Abel transform due to Rouvière and Gangolli.

MSC:
22E30 Analysis on real and complex Lie groups
43A80 Analysis on other specific Lie groups
46F99 Distributions, generalized functions, distribution spaces
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