SUFFICIENT CONDITION FOR THE DIFFERENTIABILITY OF THE RIESZ-NAGY-TAKACS SINGULAR FUNCTION
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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.
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.
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