Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

PROPERTIES OF DUAL RIESZ-NÁGY-TAKÁCS DISTRIBUTIONS

  • Baek, In-Soo (Department of Mathematics, Pusan University of Foreign Studies)
  • Received : 2008.08.27
  • Accepted : 2008.10.13
  • Published : 2008.12.25
Download PDF
⟨ Previous Next ⟩

Abstract

We give the relation between the Riemann-Stieltjes integrals with respect to the Riesz-N$\'{a}$gy-Tak$\'{a}$cs(RNT) distribution $H_{a,p}$ satisfying the equation a = $(1-a)^m$ and those with respect to the dual RNT distribution $H_{1-a,1-p}$, which leads to a generalization of recent results for a = $\frac{1}{2}$.

Keywords

References

  1. I. S. Baek, Dimensions of distribution sets in the unit interval, Comm. Korean Math. Soc., 22 no. 4 (2007), pp. 547-552. https://doi.org/10.4134/CKMS.2007.22.4.547
  2. I. S. Baek, Some properties of the Riesz-Nagy-Takacs distribution, Honam Math. Journal, 30 no. 2 (2008), pp. 227-231. https://doi.org/10.5831/HMJ.2008.30.2.227
  3. I. S. Baek, A note on the moments of the Riesz-Nagy-Takacs distribution, J. Math. Anal. Appl., 348 no. 1 (2008), pp. 165-168. https://doi.org/10.1016/j.jmaa.2008.07.014
  4. I. S. Baek. Multifractal characterization of the Riesz-Nagy-Takacs function, preprint.
  5. I. S. Baek, L. Olsen and N. Snigireva, Divergence points of self-similar measures and packing dimension, Adv. Math., 214 no. 1 (2007), pp. 267-287. https://doi.org/10.1016/j.aim.2007.02.003
  6. K.J. Falconer, Techniques in fractal geometry, John Wiley and Sons (1997).
  7. W. Goh and J. Wimp, Asymptotics for the Moments of Singular Distributions, Journal of Approximation Theory, 74 no. 3 (1993), pp. 301-334. https://doi.org/10.1006/jath.1993.1068
  8. P. J. Grabner and H. Prodinger, Asymptotic analysis of the moments of the Cantor distribution, Statistics and Probability Letters, 26 no. 3 (1996), pp. 243-248. https://doi.org/10.1016/0167-7152(95)00016-X
  9. F. R. Lad and W. F. C. Taylor, The moments of the Cantor distribution, Statistics and Probability Letters, 13 no. 4 (1992), pp. 307-310. https://doi.org/10.1016/0167-7152(92)90039-8
  10. J. Paradis, P. Viader a nd L. Bibiloni, Rlesz-Nagy singular functions revisited. J. Math. Anal. Appl., 329 (2007), pp. 592-602. https://doi.org/10.1016/j.jmaa.2006.06.082