We investigate the size of monic, orthogonal polynomials defined on the unit circle
corresponding to a finite positive measure. We find an upper bound for the
growth of these polynomials. Then we show, by example, that this upper bound can
be achieved. Throughout these proofs, we use a method developed by Rahmanov to
compute the polynomials in question. Finally, we find an explicit formula for a
subsequence of the Verblunsky coefficients of the polynomials.
Keywords
OPUC, classical analysis, approximation theory, orthogonal
polynomials on the unit circle