On planar sampling with Gaussian kernel in spaces of bandlimited functions

Let $I=(a,b)\times(c,d)\subset {\mathbb R}_{+}^2$ be an index set and let $\{G_α(x) \}_{α\in I}$ be a collection of Gaussian functions, i.e. $G_α(x) = \exp(-α_1 x_1^2 - α_2 x_2^2)$, where $α= (α_1, α_2) \in I, \, x = (x_1, x_2) \in {\mathbb R}^2$. We present a complete description of the uniformly discrete sets $Λ\subset {\mathbb R}^2$ such that every bandlimited signal $f$ admits a stable reconstruction from the samples $\{f \ast G_α (λ)\}_{λ\in Λ}$.

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