ASYMPTOTIC-BEHAVIOR OF ORTHOGONAL POLYNOMIALS CORRESPONDING TO MEASURE WITH DISCRETE PART OFF THE UNIT-CIRCLE

For a positive measure mu on the unit circle (Gamma) in the complex plane, m points Z(j) off Gamma and m positive numbers A(j), j = 1, 2,..., m, we investigate the asymptotic behavior of orthonormal polynomials Phi(n)(z) corresponding to d mu/2 pi + Sigma(j=1)(m)A(j) delta(zj), where delta(z) denotes the unit measure supported at point z. Our main result is the relative asymptotics of Phi(n)(z) with respect to the orthonormal polynomial corresponding to d mu/(2 pi) off and on Gamma. (C) 1994 Academic Press, Inc.