The moments of the Riesz-N{\'a}gy-Tak{\'a}cs distribution over a general interval
Bull. Korean Math. Soc. 2010 Vol. 47, No. 1, 187-193
https://doi.org/10.4134/BKMS.2010.47.1.187
Printed January 1, 2010
In Soo Baek
Pusan University of Foreign Studies
Abstract : In this paper, the moments of the Riesz-N{\'a}gy-Tak{\'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.
Keywords : Riemann-Stieltjes integral, moment, interval of orthogonality, singular distribution function, metric number theory
MSC numbers : Primary 26A30; Secondary 28A80
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