Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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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.

The moments of the Riesz-N{\'a}gy-Tak{\'a}cs distribution over a general interval

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