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We present the range theorem for the Radon transform for double fibrations ofthe horocycle spaces for the semisimple symmetric spaces by the invariantdifferential operators or the invariant system of differential operatorsconstructed from the action of the transformation group. This theorem alsoimplies the range theorem for the Radon transform for double fibrations ofnon-symmetric compact homogeneous spaces.

Invariant Differential Operators and the Radon Transform on the Horocycle Spaces