Abstract. The Radon transform that integrates a function in ${\rm S}^n$, the $n$-dimensional sphere, over totally geodesic submanifolds with codimension 1, the great circles, and the dual Radon transform are investigated in this paper. Inversion formulas, range spaces and null spaces are given.

AMS Subject Classification (1991): 44A05

Keyword(s): Radon transform, spherical harmonics, elliptic geometry

Received 28 November, 1991. (Registered under 5538/2009.)