Geodesic
Horospherical Transform on Riemannian Symmetric Manifolds of Noncompact Type
Funkcionalʹnyj analiz i ego priloženiâ, Tome 42 (2008) no. 4, pp. 50-59

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We discuss I. M. Gelfand's project of rebuilding the representation theory of semisimple Lie groups on the basis of integral geometry. The basic examples are related to harmonic analysis and the horospherical transform on symmetric manifolds. Specifically, we consider the inversion of this transform on Riemannian symmetric manifolds of noncompact type. In the known explicit inversion formulas, the nonlocal part essentially depends on the type of the root system. We suggest a universal modification of this operator.
Keywords: symmetric manifold, horospherical transform
Mots-clés : inversion formula, Plancherel formula. 
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     author = {S. G. Gindikin},
     title = {Horospherical {Transform} on {Riemannian} {Symmetric} {Manifolds} of {Noncompact} {Type}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {50--59},
     publisher = {mathdoc},
     volume = {42},
     number = {4},
     year = {2008},
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     url = {http://geodesic.mathdoc.fr/item/FAA_2008_42_4_a3/}
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S. G. Gindikin. Horospherical Transform on Riemannian Symmetric Manifolds of Noncompact Type. Funkcionalʹnyj analiz i ego priloženiâ, Tome 42 (2008) no. 4, pp. 50-59. http://geodesic.mathdoc.fr/item/FAA_2008_42_4_a3/