A reconstruction theorem for Riemannian symmetric spaces of noncompact type (Q2655137)

In the paper under review the author proves an analogue of the classical Whittaker-Kotelnikov-Shannon sampling theorem for Riemannian symmetric spaces of noncompact type. Let \(X\) be a Riemannian symmetric space of noncompact type and \(f\) be a rapidly decreasing radial function on \(X\) whose spherical Fourier transform has compact support. The author proves a reconstruction theorem which recovers \(f\) from the values of an integral operator applied to \(F\) on a discrete subset. It is not a direct analog of the sampling theorem, since it does not reconstruct from samples of the function itself. In the case when \(X\) is of complex type the author proves a sampling formula recovering \(f\) from its own values on a discrete set. Also, the author gives explicit results for three dimensional hyperbolic space.