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- W1978064767 abstract "If n = p + q + 1, the affine Grassmann manifolds G ( p , n ) of p -planes and G ( q , n ) of q -planes in R n are dual homogeneous spaces of the Euclidean motion group M ( n ), with ξ ϵ G ( p , n ) and η ϵ G ( q , n ) being incident if and only if ξ meets η at a right angle. The resulting integral transform from functions on G ( p , n ) to functions on G ( q , n ) generalizes both the classical Radon transform and its dual. We show that this transform intertwines the actions of certain M(n) -invariant differential operators on G ( p , n ) and G ( q , n ), and we prove an inversion formula for this transform when n is odd, generalizing the Radon inversion formula, and obtaining in particular an inversion formula for the dual transform." @default.
- W1978064767 created "2016-06-24" @default.
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- W1978064767 date "1987-04-01" @default.
- W1978064767 modified "2023-09-23" @default.
- W1978064767 title "Radon transforms on Grassmann manifolds" @default.
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- W1978064767 doi "https://doi.org/10.1016/0022-1236(87)90008-5" @default.
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