Geodesic
Asymptotics for the Radon transform on hyperbolic spaces
Vestnik rossijskih universitetov. Matematika, Tome 24 (2019) no. 127, pp. 241-251 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {2019},
     volume = {24},
     number = {127},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTAMU_2019_24_127_a0/}
}
TY  - JOUR
AU  - N. B. Andersen
AU  - M. Flensted-Jensen
TI  - Asymptotics for the Radon transform on hyperbolic spaces
JO  - Vestnik rossijskih universitetov. Matematika
PY  - 2019
SP  - 241
EP  - 251
VL  - 24
IS  - 127
UR  - http://geodesic.mathdoc.fr/item/VTAMU_2019_24_127_a0/
LA  - ru
ID  - VTAMU_2019_24_127_a0
ER  - 
%0 Journal Article
%A N. B. Andersen
%A M. Flensted-Jensen
%T Asymptotics for the Radon transform on hyperbolic spaces
%J Vestnik rossijskih universitetov. Matematika
%D 2019
%P 241-251
%V 24
%N 127
%U http://geodesic.mathdoc.fr/item/VTAMU_2019_24_127_a0/
%G ru
%F VTAMU_2019_24_127_a0
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/

[1] N. B. Andersen, M. Flensted-Jensen and H. Schlichtkrull, “Cuspidal discrete series for semisimple symmetric spaces”, Journal of Functional Analysis, 263:8 (2012), 2384–2408 | DOI | MR | Zbl

[2] N. B. Andersen, M. Flensted-Jensen, “Cuspidal discrete series for projective hyperbolic spaces”, Contemporary Mathematics, v. 598, Geometric Analysis and Integral Geometry, Amer Mathematical Society, Providence, 2013, 59–75 | DOI | MR | Zbl