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Let $\lambda$ be a positive number, and let $(x_j:j\in\mathbbZ)\subset\mathbb R$ be a fixed Riesz-basis sequence, namely, $(x_j)$ isstrictly increasing, and the set of functions $\{\mathbb R\ni t\mapstoe^{ix_jt}:j\in\mathbb Z\}$ is a Riesz basis ({\it i.e.,} unconditionalbasis)for $L_2[-\pi,\pi]$. Given a function $f\in L_2(\mathbb R)$ whose Fouriertransform is zero almost everywhere outside the interval $[-\pi,\pi]$, there isa unique square-summable sequence $(a_j:j\in\mathbb Z)$, depending on $\lambda$and $f$, such that the function$$I_\lambda(f)(x):=\sum_{j\in\mathbbZ}a_je^{-\lambda(x-x_j)^2}, \qquad x\in\mathbb R, $$ is continuous and squareintegrable on $(-\infty,\infty)$, and satisfies the interpolatory conditions$I_\lambda (f)(x_j)=f(x_j)$, $j\in\mathbb Z$. It is shown that $I_\lambda(f)$converges to $f$ in $L_2(\mathbb R)$, and also uniformly on $\mathbb R$, as$\lambda\to0^+$. A multidimensional version of this result is also obtained. Inaddition, the fundamental functions for the univariate interpolation processare defined, and some of their basic properties, including their exponentialdecay for large argument, are established. It is further shown that theassociated interpolation operators are bounded on $\ell_p(\mathbb Z)$ for every$p\in[1,\infty]$.

On the sampling and recovery of bandlimited functions via scattered translates of the Gaussian