Sufficient condition for the differentiability of the Riesz-N{\'a}gy-Tak{\'a}cs singular function
Bull. Korean Math. Soc. 2017 Vol. 54, No. 4, 1173-1183
https://doi.org/10.4134/BKMS.b160267
Published online July 31, 2017
In-Soo Baek
Busan University of Foreign Studies
Abstract : We give some sufficient conditions for the null and infinite derivatives of the Riesz-N{\'a}gy-Tak{\'a}cs (RNT) singular function. Using these conditions, we show that the Hausdorff dimension of the set of the infinite derivative points of the RNT singular function coincides with its packing dimension which is positive and less than 1 while the Hausdorff dimension of the non-differentiability set of the RNT singular function does not coincide with its packing dimension 1.
Keywords : singular function, Hausdorff dimension, packing dimension, self-similar set, distribution set, non-differentiability, metric number theory
MSC numbers : Primary 26A30; Secondary 28A78
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