ACTA issues

## The range of the Radon transform on the real hyperbolic Grassmann manifold

Satoshi Ishikawa

Acta Sci. Math. (Szeged) 86:1-2(2020), 225-264
23/2019

 Abstract. Let $\Gamma ^n_k$ be the space of all the $k$-dimensional totally geodesic submanifolds of the $n$-dimensional real hyperbolic space where $1\leq k\leq n-1$. We prove that the Radon transform $R$ for double fibrations of the real hyperbolic Grassmann manifolds $\Gamma ^n_p$ and $\Gamma ^n_q$ with respect to the inclusion incidence relations maps $C^\infty _0(\Gamma ^n_p)$ bijectively onto the space of all the functions in $C^\infty _0(\Gamma ^n_q)$ which satisfy a certain system of linear partial differential equations explicitly constructed from the left infinitesimal action of the transformation group when \$0\leq p