Formulas for the Walsh coefficients of smooth functions and their application to bounds on the Walsh coefficients

摘要

We establish formulas for the b-adic Walsh coefficients of functions in C-alpha[0, 1] for an integer alpha >= 1 and give upper bounds on the Walsh coefficients of these functions. We also study the Walsh coefficients of periodic and non-periodic functions in reproducing kernel Hilbert spaces. (C) 2016 Elsevier Inc. All rights reserved.