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Mathematics  2013 

The decay of the Walsh coefficients of smooth functions

DOI: 10.1017/S0004972709000392

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Abstract:

We give upper bounds on the Walsh coefficients of functions for which the derivative of order at least one has bounded variation of fractional order. Further, we also consider the Walsh coefficients of functions in periodic and non-periodic reproducing kernel Hilbert spaces. A lower bound which shows that our results are best possible is also shown.

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