Nonuniform sampling and recovery of bandlimited functions in higher dimensions

We provide sufficient conditions on a family of functions (ϕα)α∈A:Rd→R for sampling of multivariate bandlimited functions at certain nonuniform sequences of points in Rd. We consider interpolation of functions whose Fourier transform is supported in some small ball in Rd at scattered points (xj)j∈N such that the complex exponentials (e−i〈xj,⋅〉)j∈N form a Riesz basis for the L2 space of a convex body containing the ball. Recovery results as well as corresponding approximation orders in terms of the parameter α are obtained.