Before revision: We construct deep ReLU neural networks to approximate functions in dilated shift-invariant spaces generated by a continuous function with compact support and study the approximation rates with respect to the number of neurons .
After revision: We construct deep ReLU neural networks to approximate functions in dilated shift-invariant spaces , which are widely used in signal processing, image processing, communications and so on. Approximation error bounds are estimated with respect to the number of neurons .