Journal of approximation theory vol:96 issue:1 pages:1-32
Orthogonal polynomials on the unit circle are fully determined by their reflection coefficients through the Szego recurrences. Assuming that the reflection coefficients converge to a complex number a with 0 < \a\<1, or, in addition, they form a sequence of bounded variation, we analyze the orthogonal polynomials by comparing them with orthogonal polynomials with constant reflection coefficients which were studied earlier by Ya. L. Geronimus and N. I. Akhiezer. In particular, we present asymptotic relations under certain assumptions on the rate of convergence of the reflection coefficients. Under weaker conditions we still obtain useful information about the orthogonal polynomials and also about the measure of orthogonality. (C) 1999 Academic Press.