Spherical means in annular regions in the n-dimensional real hyperbolic spaces

Abstract

Let Z r,R be the class of all continuous functions f on the annulus Ann(r, R) in the real hyperbolic space B n with spherical means M s f (x) = 0, whenever s > 0 and x ∈ B n are such that the sphere S s (x) ⊂ Ann(r, R) and B r (o) ⊆ B s (x). In this article, we give a characterization for functions in Z r,R . In the case R = ∞, this result gives a new proof of Helgason's support theorem for spherical means in the real hyperbolic spaces.