Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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SOME PROPERTIES OF THE RIESZ-NÁGY-TAKÁCS DISTRIBUTION

  • Baek, In-Soo (Department of Mathematics, Pusan University of Foreign Studies)
  • Received : 2007.11.13
  • Accepted : 2008.05.19
  • Published : 2008.06.25
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Abstract

We give some 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 1 - a = $a^m$ over different intervals, which generalizes recent results([6]) for a = ${\frac{1}{2}}$.

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References

  1. I. S. Baek, Dimensions of distribution sets in the unit interval, Comm. Korean Math. Soc. 22(4) (2007), 547-552. https://doi.org/10.4134/CKMS.2007.22.4.547
  2. I. S. Baek, Multifractal characterization of the Riesz-Nagy-Takacs function, preprint.
  3. I. S. Baek, A note on the moments of the Riesz-Nagy-Takacs distribution, preprint.
  4. I. S. Baek, L. Olsen and N. Snigireva, Divergence points of self-similar measures and packing dimension, Adv. Math. 214(1) (2007), 267-287. https://doi.org/10.1016/j.aim.2007.02.003
  5. K.J. Falconer, Techniques in fractal geometry, John Wiley and Sons (1997).
  6. W. Goh and J. Wimp, Asymptotics for the Moments of Singular Distributions, Journal of Approximation Theory 74(3) (1993), 301-334. https://doi.org/10.1006/jath.1993.1068
  7. P. J. Grabner and H. Prodinger, Asymptotic analysis of the moments of the Cantor distribution, Statistics and Probability Letters 26(3) (1996), 243-248. https://doi.org/10.1016/0167-7152(95)00016-X
  8. F. R. Lad and W. F. C. Taylor, The moments of the Cantor distribution, Statistics and Probability Letters, 13(4) (1992), 307-310. https://doi.org/10.1016/0167-7152(92)90039-8
  9. J. Paradis, P. Viader and L. Bibiloni, Riesz-Nagy singular functions revisited, J. Math. Anal. Appl. 329 (2007), 592-602. https://doi.org/10.1016/j.jmaa.2006.06.082

Cited by

  1. PROPERTIES OF DUAL RIESZ-NÁGY-TAKÁCS DISTRIBUTIONS vol.30, pp.4, 2008, https://doi.org/10.5831/HMJ.2008.30.4.671