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

We establish formulas for the bb-adic Walsh coefficients of functions in Cα[0,1]Cα[0,1] for an integer α≥1α≥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.