International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 2, Pages 255-258
doi:10.1155/S0161171293000298

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

Abstract

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.