Abstract: A symmetric space is a homogeneous space G/H for a Lie group G of a specific kind. Examples of symmetric spaces are spheres, Euclidean spaces and hyperbolic spaces, such as the de Sitter and the anti de Sitter space. For each symmetric space there exists a class of submanifolds called horospheres. A horosphere is an orbit in G/H of a unipotent subgroup of G of a certain type. The horospherical transform is a Radon transform that maps a function on G/H to a function on the set of horospheres. The value of a transformed function at a given horosphere is defined to be the integral of that function over that horosphere. I will present a support theorem for the horospherical transform which describes the support of a function in terms of the support of the transformed function. This result generalizes the support theorem of Helgason for the horospherical transform on Riemannian symmetric spaces.
