Abstract
We examine for the first time the strong derivative on quasi-normed linear spaces. We show for a large class of such spaces (including Lp[0,1), 0<p<1, and the block spaces Bq, q≥1) that a Walsh series which converges fast enough is term by term strongly differentiable. We also investigate the case of term by term pointwise dyadic differentiation on the interval[0,1).
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This research supported in part by a National Science Foundation grant INT-8620153
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Powell, C.H., Wade, W.R. Term by term dyadic differentiation of rapidly convergent Walsh series. Approx. Theory & its Appl. 7, 20–40 (1991). https://doi.org/10.1007/BF02845189
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DOI: https://doi.org/10.1007/BF02845189