International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 2, Pages 255-258

Remarks on orthogonal polynomials with respect to varying measures and related problems

Xin Li

Department of Mathematics, University of Central Florida, Orlando 32816, FL, USA

Received 26 March 1992; Revised 4 May 1992

Copyright © 1993 Xin Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We point out the relation between the orthogonal polynomials with respect to (w.r.t.) varying measures and the so-called orthogonal rationals on the unit circle in the complex plane. This observation enables us to combine different techniques in the study of these polynomials and rationals. As an example, we present a simple and short proof for a known result on the weak-star convergence of orthogonal polynomials w.r.t, varying measures. Some related problems are also considered.