Sampling theorems on bounded domains

This paper concerns with iterative schemes for the perfect reconstruction from nonuniform sampling of functions belonging to multiresolution spaces on bounded manifolds. Since the iterations converge uniformly, we can produce the corresponding iterative integration schemes that allow to recover the integral of functions belonging to multiresolution spaces from nonuniform sampling. We present also an error analysis and, in particular, we estimate the L2-error we produce in recovering smooth functions in Hs, but not necessarily in any multiresolution space. The error analysis extends to integrals. Our results hold regardless of the dimension of the domain and for a variety of multiresolution spaces constructed from certain refinable bases formed by the so-called GP-functions.