On the Funk transform on compact symmetric spaces

Klein, Sebastian; Thorbergsson, Gudlaugur; Verhoczki, Laszlo

On the Funk transform on compact symmetric spaces

Authors

Klein, Sebastian

Thorbergsson, Gudlaugur

Verhoczki, Laszlo

Description

We prove that a function on an irreducible compact symmetric space M, which is not a sphere, is determined by its integrals over the shortest closed geodesics in M. We also prove a support theorem for the Funk transform on rank one symmetric spaces which are not spheres.
8 pages