Rational approximants associated with measures supported on the unit circle and the real line

摘要

As a continuation of the well known connection between the theory of orthogonal polynomials on the unit circle and the interval [−1,1], in this paper properties concerning error and convergence of certain rational approximants associated with the measures dμ(t) and dσ(θ)=|dμ(cosθ)| supported on [−1,1] and the unit circle respectively are deduced. Numerical illustrations are also given.