The spherical mean value operator for compact symmetric spaces (Q1901171)

The authors determine the eigenvalues of the mean value operator over geodesic spheres of fixed radius for compact symmetric spaces of arbitrary rank. This way they obtain a new proof of an earlier result of Sunada on ergodicity of the mean value operator in these spaces. The reviewer considered this problem for the Heisenberg group [\textit{M. Agranovsky}, \textit{C. Berenstein} and \textit{D.-C. Chang}, Ergodic and mixing properties of radial measures on the Heisenberg group, in ``Fourier Analysis: analytic and geometric aspects'', W. O. Bray et al., eds., Lect. Notes Pure Appl. Math. 157, 1-15 (1994)] and would like to point out that Marc-Olivier Gebuhrer obtained similar results for hypergroups in his unpublished doctoral thesis at Strasbourg.