Abstract
This chapter explains the relationship between Radon transforms on compact Grassmann manifolds and invariant differential operators of determinantal type. It constructs the range characterizing operator for the Radon transform on the real Grassmann manifold. The invariant differential operators of determinantal type play an important role not only in the range characterizations but also in the construction of inversion formulas. In addition to real Grassmann manifolds, there are two kinds of Grassmann manifolds, complex Grassmann manifolds and quaternionic Grassmann manifolds.
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