ON THE DISTRIBUTION OF ZEROS OF POLYNOMIALS ORTHOGONAL ON THE UNIT-CIRCLE

Let {Φn} be a system of monic polynomials orthogonal on the unit circle with respect to a positive Borel measure μ. It is shown that under fairly mild conditions on the reflection coefficients, Φn(0), the zeros of a subsequence of {Φn} are asymptotically uniformly distributed on some circle. The radius of this circle can be found using a Cauchy-Hadamard-type formula. We also characterize the measures μ with the property that the Ldμ2 best polynomial approximants to every function f ε{lunate} H2(μ) converge uniformly on every compact subset of the open unit disc at a geometrically fast rate. © 1990.