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http://dx.doi.org/10.4134/BKMS.b160267

SUFFICIENT CONDITION FOR THE DIFFERENTIABILITY OF THE RIESZ-NÁGY-TAKÁCS SINGULAR FUNCTION  

Baek, In-Soo (Department of Mathematics Busan University of Foreign Studies)
Publication Information
Bulletin of the Korean Mathematical Society / v.54, no.4, 2017 , pp. 1173-1183 More about this Journal
Abstract
We give some sufficient conditions for the null and infinite derivatives of the $Riesz-N{\acute{a}}gy-Tak{\acute{a}}cs$ (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;
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Times Cited By KSCI : 1  (Citation Analysis)
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