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 $$\{G_{\alpha }(x) \}_{\alpha \in I}$$ a collection of Gaussian functions, i.e. $$G_{\alpha = \exp (-\alpha _1 x_1^2 - \alpha _2 x_2^2)$$ , where $$\alpha (\alpha _1, _2) I, \, x (x_1, x_2) R}^2$$ . We present complete description the uniformly discrete sets $$\Lambda \subset such that every bandlimited signal f admits stable reconstruction from samples $$\{f *G_{\alpha } (\lambda )\}_{\lambda \Lambda }$$