ON ORTHOGONAL POLYNOMIALS WITH RESPECT TO VARYING MEASURES ON THE UNIT-CIRCLE

Let {phi(n)(dmu)} be a system of orthonormal polynomials on the unit circle with respect to dmu and {psi(n, m)(dmu)} be a system of orthonormal polynomials on the unit circle with respect to the varying measures dmu/\w(n)(z)\2, z = e(itheta), where {w(n)(z)} is a sequence of polynomials, deg w(n) = n, whose zeros w(n), 1, ..., w(n, n) lie in \z\ < 1 The asymptotic behavior of the ratio of the two systems on and outside the unit circle is obtained.