Geodesic
Asymptotics for the Radon transform on hyperbolic spaces
Vestnik rossijskih universitetov. Matematika, Tome 24 (2019) no. 127, pp. 241-251

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Let $G/H$ be a hyperbolic space over $\Bbb R,$ $\Bbb C$ or $\Bbb H,$ and let $K$ be a maximal compact subgroup of $G.$ Let $D$ denote a certain explicit invariant differential operator, such that the non-cuspidal discrete series belong to the kernel of $D.$ For any $L^2$-Schwartz function $f$ on $G/H,$ we prove that the Abel transform ${\mathcal A}(Df)$ of $Df$ is a Schwartz function. This is an extension of a result established in [2] for $K$-finite and $K\cap H$-invariant functions.
Keywords: hyperbolic spaces, cuspidal discrete series
Mots-clés : Radon transform, Abel transform. 
@article{VTAMU_2019_24_127_a0,
     author = {N. B. Andersen and M. Flensted-Jensen},
     title = {Asymptotics for the {Radon} transform on hyperbolic spaces},
     journal = {Vestnik rossijskih universitetov. Matematika},
     pages = {241--251},
     publisher = {mathdoc},
     volume = {24},
     number = {127},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTAMU_2019_24_127_a0/}
}
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N. B. Andersen; M. Flensted-Jensen. Asymptotics for the Radon transform on hyperbolic spaces. Vestnik rossijskih universitetov. Matematika, Tome 24 (2019) no. 127, pp. 241-251. http://geodesic.mathdoc.fr/item/VTAMU_2019_24_127_a0/