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

Title & Authors
THE MOMENTS OF THE RIESZ-NǺGY-TAKǺCS DISTRIBUTION OVER A GENERAL INTERVAL
Baek, In-Soo;

Abstract
In this paper, the moments of the Riesz-N$\small{\acute{a}}$gy-Tak$\small{\acute{a}}$cs(RNT) distribution over a general interval [a, b] $\small{\subset}$ [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.
Keywords
Riemann-Stieltjes integral;moment, interval of orthogonality;singular distribution function;metric number theory;
Language
English
Cited by
1.
GOLDEN RATIO RIESZ-N\$\acute{A}\$GY-TAK\$\acute{A}\$CS DISTRIBUTION,;

충청수학회지, 2011. vol.24. 2, pp.247-252
References
1.
I. S. Baek, Dimensions of distribution sets in the unit interval, Commun. Korean Math. Soc. 22 (2007), no. 4, 547–552.

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.

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.

5.
W. Goh and J. Wimp, Asymptotics for the moments of singular distributions, J. Approx. Theory 74 (1993), no. 3, 301–334.

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.

7.
F. R. Lad and W. F. C. Taylor, The moments of the Cantor distribution, Statist. Probab. Lett. 13 (1992), no. 4, 307–310.

8.
J. Paradıs, P. Viader, and L. Bibiloni, Riesz-Nagy singular functions revisited, J. Math. Anal. Appl. 329 (2007), no. 1, 592–602.

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.