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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.
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참고문헌 (13)
참고문헌 신청
I. S. Baek / 2008 / A note on the moments of the Riesz-N´agy-Tak´acs distribution / J. Math. Anal. Appl 348(1):165~168
백인수 / 2011 / Derivative of the Riesz-N[문자]gy-Tak[문자]cs function / 대한수학회보 48(2):261~275
I. S. Baek / 2007 / Divergence points of self-similar measures and packing dimension / Adv. Math 214(1):267~287
R. Darst / 1993 / The Hausdorff dimension of the nondifferentiability set of the Cantor function is ( ln 2ln 3 )2 / Proc. Amer. Math. Soc 119(1):105~108
R. Darst / 1995 / Hausdorff dimension of sets of non-differentiability points of Cantor functions / Math. Proc. Cambridge Philos. Soc 117(1):185~191
백인수 / 2011 / Derivative of the Riesz-N[문자]gy-Tak[문자]cs function / 대한수학회보 48(2):261~275
I. S. Baek / 2007 / Divergence points of self-similar measures and packing dimension / Adv. Math 214(1):267~287
R. Darst / 1993 / The Hausdorff dimension of the nondifferentiability set of the Cantor function is ( ln 2ln 3 )2 / Proc. Amer. Math. Soc 119(1):105~108
R. Darst / 1995 / Hausdorff dimension of sets of non-differentiability points of Cantor functions / Math. Proc. Cambridge Philos. Soc 117(1):185~191
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