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Bull. Korean Math. Soc. 2017; 54(4): 1173-1183

Online first article May 22, 2017      Printed July 31, 2017

https://doi.org/10.4134/BKMS.b160267

Copyright © The Korean Mathematical Society.

Sufficient condition for the differentiability of the Riesz-N{\'a}gy-Tak{\'a}cs singular function

In-Soo Baek

Busan University of Foreign Studies

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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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