Numerical integration of Holder continuous, absolutely convergent Fourier, Fourier cosine, and Walsh series

We introduce quasi-Monte Carlo rules for the numerical integration of functions f defined on [0, 1](s), s >= 1, which satisfy the following properties: the Fourier, Fourier cosine or Walsh coefficients of f are absolutely summable and f satisfies a Holder condition of order alpha, for some 0 < alpha <= 1. We show a convergence rate of the integration error of order max((s - 1)N-1/2, s(alpha/2)N(-alpha)). The construction of the quadrature points is explicit and is based on Weil sums. (C) 2014 Elsevier Inc. All rights reserved.