  For every $p > (1 + \sqrt{5})/2$ we construct a uniformly discrete real
sequence $\{\lambda_n\}_{n=1}^\infty$ with $|\lambda_{n+1}| > |\lambda_n|$, a
function $g \in L^p(\mathbb{R})$, and continuous linear functionals $\{g^*_n\}$
on $L^p(\mathbb{R})$, such that every $f \in L^p(\mathbb{R})$ admits a series
expansion \[ f(x) = \sum_{n=1}^{\infty} g_n^*(f) g(x-\lambda_n) \] convergent
in the $L^p(\mathbb{R})$ norm. We also prove a similar result for the space
$C_0(\mathbb{R})$, where in this case $\{\lambda_n\}_{n=1}^\infty$ is taken to
be the sequence of positive integers.
