Uniform approximation to ¦x¦β by Sinc functions

AbstractThe best uniform approximation to the function ¦x¦β, β > 0, on [−1, 1] by any of the standard classes of functions of approximation theory has an asymptotic error of at best O(e−c√n), where n is the dimension of the space of approximating functions. We exhibit a class of Sinc basis functions for which this error decays at the faster rate O(e−cnlog n), uniformly for all 0 < β0 ⩽ β ⩽ β1