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http://dx.doi.org/10.4134/BKMS.2011.48.2.261

DERIVATIVE OF THE RIESZ-NÁGY-TAKÁCS FUNCTION  

Baek, In-Soo (Department of Mathematics Pusan University of Foreign Studies)
Publication Information
Bulletin of the Korean Mathematical Society / v.48, no.2, 2011 , pp. 261-275 More about this Journal
Abstract
We give characterizations of the differentiability points and the non-differentiability points of the Riesz-N$\gy-Tak$\cs(RNT) singulr 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;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By Web Of Science : 2  (Related Records In Web of Science)
Times Cited By SCOPUS : 1
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