Convergence of ray sequences of Frobenius-Padé approximants

Let be a Cauchy transform of a possibly complex-valued Borel measure and a system of orthonormal polynomials with respect to a measure , where . An th Frobenius-Padé approximant to is a rational function , , , such that the first Fourier coefficients of the remainder function vanish when the form is developed into a series with respect to the polynomials . We investigate the convergence of the Frobenius-Padé approximants to along ray sequences , , when and are supported on intervals of the real line and their Radon-Nikodym derivatives with respect to the arcsine distribution of the corresponding interval are holomorphic functions. Bibliography: 30 titles.