In a previous post, we discussed the orthogonality properties of Walsh functions and showed that they form a complete orthonormal system in . In this post we discuss the rate of decay of the Walsh coefficients when the function has bounded variation of fractional order and we investigate pointwise convergence of the Walsh series and pointwise convergence of the Walsh series to the function. We consider only Walsh functions in base although the results can be generalized to Walsh functions over groups. Information on Walsh functions over groups can be found in this post. For the necessary background information see the previous post on Walsh functions here. A table of contents for the posts on Walsh functions can be found here. Continue reading

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