On Planar Sampling with Gaussian Kernel in Spaces of Bandlimited Functions

Let I=(a,b)× (c,d)⊂ℝ_+^2 be an index set and let {G_α(x) }_α∈ I be a collection of Gaussian functions, i.e. G_α(x) = exp (-α _1 x_1^2 - α _2 x_2^2) , where α = (α _1, α _2) ∈ I, x = (x_1, x_2) ∈ℝ^2 . We present a complete description of the uniformly discrete sets Λ⊂ℝ^2 such that every bandlimited signal f admits a stable reconstruction from the samples {f *G_α (λ )}_λ∈Λ .