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 .