Geodesic
Horospherical Transform on Real Symmetric Varieties: Kernel and Cokernel
Funkcionalʹnyj analiz i ego priloženiâ, Tome 43 (2009) no. 1, pp. 37-54

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In this paper, we define a horospherical transform for a semisimple symmetric space $Y$. A natural double fibration is used to assign a more geometrical space $\Xi$ of horospheres to $Y$. The horospherical transform relates certain integrable analytic functions on $Y$ to analytic functions on $\Xi$ by fiber integration. We determine the kernel of the horospherical transform and establish that the transform is injective on functions belonging to the most continuous spectrum of $Y$.
Keywords: semisimple symmetric space, horospherical transform, Plancherel theorem.
Mots-clés : Fourier transform 
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     author = {B. Kr\"otz},
     title = {Horospherical {Transform} on {Real} {Symmetric} {Varieties:} {Kernel} and {Cokernel}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {37--54},
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     url = {http://geodesic.mathdoc.fr/item/FAA_2009_43_1_a2/}
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B. Krötz. Horospherical Transform on Real Symmetric Varieties: Kernel and Cokernel. Funkcionalʹnyj analiz i ego priloženiâ, Tome 43 (2009) no. 1, pp. 37-54. http://geodesic.mathdoc.fr/item/FAA_2009_43_1_a2/