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

Abstract

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 d μ ( t ) and d σ ( θ ) = | d μ ( cos θ ) | supported on [ − 1 , 1 ] and the unit circle respectively are deduced. Numerical illustrations are also given.