Derivative of the Riesz-N{\'a}gy-Tak{\'a}cs function
Bull. Korean Math. Soc. 2011 Vol. 48, No. 2, 261-275
https://doi.org/10.4134/BKMS.2011.48.2.261
Printed March 1, 2011
In-Soo Baek
Pusan University of Foreign Studies
Abstract : We give characterizations of the differentiability points and the non-differentiability points of the Riesz-N{\'a}gy-Tak{\'a}cs(RNT) singular function using the distribution sets in the unit interval. Using characterizations, we show that the Hausdorff dimension of the non-differentiability points of the RNT singular function is greater than $0$ and the packing dimension of the infinite derivative points of the RNT singular function is less than $1$. Further the RNT singular function is nowhere differentiable in the sense of topological magnitude, which leads to that the packing dimension of the non-differentiability points of the RNT singular function is 1. Finally we show that our characterizations generalize a recent result from the $(\tau, \tau -1)$-expansion associated with the RNT singular function adding a new result for a sufficient condition for the non-differentiability points.
Keywords : Hausdorff dimension, packing dimension, distribution set, local dimension set, singular function, metric number theory
MSC numbers : 26A30, 28A80
Downloads: Full-text PDF  


Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd