Bulletin of the Korean Mathematical Society (대한수학회보)

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THE MOMENTS OF THE RIESZ-NǺGY-TAKǺCS DISTRIBUTION OVER A GENERAL INTERVAL

  • Baek, In-Soo (Department of Mathematics, Pusan University of Foreign Studies)
  • Published : 2010.01.31
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Abstract

In this paper, the moments of the Riesz-N$\acute{a}$gy-Tak$\acute{a}$cs(RNT) distribution over a general interval [a, b] $\subset$ [0, 1], are found through the moments of the RNT distribution over the unit interval, [0, 1]. This is done using some special features of the distribution and the fact that [0, 1] is a self-similar set in a dynamical system generated by the RNT distribution. The results are important for the study of the orthogonal polynomials with respect to the RNT distribution over a general interval.

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References

  1. I. S. Baek, Dimensions of distribution sets in the unit interval, Commun. Korean Math. Soc. 22 (2007), no. 4, 547–552. https://doi.org/10.4134/CKMS.2007.22.4.547
  2. I. S. A note on the moments of the Riesz-N´agy-Tak´acs distribution, J. Math. Anal. Appl. 348 (2008), no. 1, 165–168. https://doi.org/10.1016/j.jmaa.2008.07.014
  3. K. J. Falconer, Techniques in Fractal Geometry, John Wiley & Sons, Ltd., Chichester, 1997.
  4. H. Fischer, On the paper: “Asymptotics for the moments of singular distributions” [J. Approx. Theory 74 (1993), no. 3, 301–334] by W. Goh and J. Wimp, J. Approx. Theory 82 (1995), no. 3, 362–374. https://doi.org/10.1006/jath.1995.1085
  5. W. Goh and J. Wimp, Asymptotics for the moments of singular distributions, J. Approx. Theory 74 (1993), no. 3, 301–334. https://doi.org/10.1006/jath.1993.1068
  6. P. J. Grabner and H. Prodinger, Asymptotic analysis of the moments of the Cantor distribution, Statist. Probab. Lett. 26 (1996), no. 3, 243–248. https://doi.org/10.1016/0167-7152(95)00016-X
  7. F. R. Lad and W. F. C. Taylor, The moments of the Cantor distribution, Statist. Probab. Lett. 13 (1992), no. 4, 307–310. https://doi.org/10.1016/0167-7152(92)90039-8
  8. J. Paradıs, P. Viader, and L. Bibiloni, Riesz-Nagy singular functions revisited, J. Math. Anal. Appl. 329 (2007), no. 1, 592–602. https://doi.org/10.1016/j.jmaa.2006.06.082
  9. W. Rudin, Principles of Mathematical Analysis, Third edition. International Series in Pure and Applied Mathematics. McGraw-Hill Book Co., New York-Auckland-Dusseldorf, 1976.