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SINGULARITY ORDER OF THE RIESZ-NÁGY-TAKÁCS FUNCTION
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 Title & Authors
SINGULARITY ORDER OF THE RIESZ-NÁGY-TAKÁCS FUNCTION
Baek, In-Soo;
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 Abstract
We give the characterization of Hlder differentiability points and non-differentiability points of the Riesz-Ngy-Takcs (RNT) singular function satisfying ${\Psi}_{a,p}(a)
 Keywords
Hausdorff dimension;packing dimension;distribution set;local dimension set;singular function;metric number theory;Hlder derivative;
 Language
English
 Cited by
 References
1.
I. S. Baek, Relation between spectral classes of a self-similar Cantor set, J. Math. Anal. Appl. 292 (2004), no. 1, 294-302. crossref(new window)

2.
I. S. Baek, Dimensions of distribution sets in the unit interval, Commun. Korean Math. Soc. 22 (2007), no. 4, 547-552. crossref(new window)

3.
I. S. Baek, Multifractal spectrum in a self-similar attractor in the unit interval, Commun. Korean Math. Soc. 23 (2008), no. 4, 549-554. crossref(new window)

4.
I. S. Baek, Derivative of the Riesz-Nagy-Takacs function, Bull. Korean Math. Soc. 48 (2011), no. 2, 261-275. crossref(new window)

5.
I. S. Baek, L. Olsen, and N. Snigireva, Divergence points of self-similar measures and packing dimension, Adv. Math. 214 (2007), no. 1, 267-287. crossref(new window)

6.
P. Billingsley, Probability and Measure, John Wiley and Sons, 1995.

7.
C. D. Cutler, A note on equivalent interval covering systems for Hausdorff dimension on ${\mathbb{R}}$, Intern. J. Math. Math. Sci. 11 (1988), no. 4, 643-649. crossref(new window)

8.
R. Darst, The Hausdorff dimension of the non-differentiability set of the Cantor function is $(\frac{ln\;2}{ln\;3})^2$, Proc. Amer. Math. Soc. 119 (1993), no. 1, 105-108.

9.
R. Darst, Hausdorff dimension of sets of non-differentiability points of Cantor functions, Math. Proc. Cambridge Philos. Soc. 117 (1995), no. 1, 185-191. crossref(new window)

10.
J. Eidswick, A characterization of the non-differentiability set of the Cantor function, Proc. Amer. Math. Soc. 42 (1974), 214-217. crossref(new window)

11.
K. J. Falconer, Techniques in Fractal Geometry, John Wiley and Sons, 1997.

12.
M. Kessebohmer and B. O. Stratmann, Holder-differentiability of Gibbs distribution functions, Math. Proc. Cambridge Philos. Soc. 147 (2009), no. 2, 489-503. crossref(new window)

13.
H. H. Lee and I. S. Baek, A note on equivalent interval covering systems for packing dimension of ${\mathbb{R}}$, J. Korean Math. Soc. 28 (1991), no. 2, 195-205.

14.
L. Olsen, Extremely non-normal numbers, Math. Proc. Cambridge Philos. Soc. 137 (2004), no. 1, 43-53. crossref(new window)

15.
L. Olsen and S. Winter, Normal and non-normal points of self-similar sets and divergence points of self-similar measures, J. London Math. Soc. (2) 67 (2003), no. 1, 103-122. crossref(new window)

16.
J. Paradis, P. Viader, and L. Bibiloni, The derivative of Minkowski's ?(x) function, J. Math. Anal. Appl. 253 (2001), no. 1, 107-125. crossref(new window)

17.
J. Paradis, P. Viader, and L. Bibiloni, Riesz-Nagy singular functions revisited, J. Math. Anal. Appl. 329 (2007), no. 1, 592-602. crossref(new window)

18.
H. L. Royden, Real Analysis, Macmillan Publishing Company, 1988.