UNIFORM APPROXIMATION TO /X/-BETA BY SINC FUNCTIONS

The 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 -cn log n), uniformly for all 0 < β0 ≤ β ≤ β1. © 1991.