Bull. Korean Math. Soc. 2010; 47(1): 187-193
Printed January 1, 2010
https://doi.org/10.4134/BKMS.2010.47.1.187
Copyright © The Korean Mathematical Society.
In Soo Baek
Pusan University of Foreign Studies
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
2018; 55(3): 679-698
2017; 54(4): 1173-1183
2011; 48(2): 261-275
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd