Geodesic
On the Kernel of the Maximal Flat Radon Transform on Symmetric Spaces of Compact Type
Journal of Lie theory, Tome 27 (2017) no. 3, pp. 623-636
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Let $M$ be a Riemannian globally symmetric space of compact type, $M'$ its set of maximal flat totally geodesic tori, and Ad$(M)$ its adjoint space. We show that the kernel of the maximal flat Radon transform $\tau\colon L^2(M) \rightarrow L^2(M')$ is precisely the orthogonal complement of the image of the pullback map $L^2({\rm Ad}(M))\rightarrow L^2(M)$. In particular, we show that the maximal flat Radon transform is injective if and only if $M$ coincides with its adjoint space.
Classification : 44A12, 22E30, 22E46, 43A85, 53C35, 53C65
Mots-clés : Integral geometry, Radon transform, symmetric space 
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     author = {E. L. Grinberg and S. G. Jackson},
     title = {On the {Kernel} of the {Maximal} {Flat} {Radon} {Transform} on {Symmetric} {Spaces} of {Compact} {Type}},
     journal = {Journal of Lie theory},
     pages = {623--636},
     year = {2017},
     volume = {27},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JLT_2017_27_3_JLT_2017_27_3_a0/}
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E. L. Grinberg; S. G. Jackson. On the Kernel of the Maximal Flat Radon Transform on Symmetric Spaces of Compact Type. Journal of Lie theory, Tome 27 (2017) no. 3, pp. 623-636. http://geodesic.mathdoc.fr/item/JLT_2017_27_3_JLT_2017_27_3_a0/