Locally constant dyadic derivatives |
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Authors: | W R Wade |
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Institution: | (1) Mathematics Department, University of Tennessee, 37916 Knoxville, TN, USA |
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Abstract: | We show that in order for a Walsh series to be locally constant it is necessary for certain blocks of that series to sum to zero. As a consequence, we show that a functionf with a somewhat sparse Walsh—Fourier series is necessarily a Walsh polynomial if its strong dyadic derivative is constant on an interval. In particular, if a Rademacher seriesR is strongly dyadically differentiable and if that derivative is constant on any open subset of 0, 1], thenR is a Rademacher polynomial. |
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Keywords: | Primary 42A56 |
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