2 research outputs found
Szeg\H{o}-type asymptotics for ray sequences of Frobenius-Pad\'e approximants
Let be a Cauchy transform of a possibly complex-valued Borel
measure and be a system of orthonormal polynomials with
respect to a measure ,
. An -th
Frobenius-Pad\'e approximant to is a rational function ,
, , such that the first
Fourier coefficients of the linear form vanish when the
form is developed into a series with respect to the polynomials . We
investigate the convergence of the Frobenius-Pad\'e approximants to
along ray sequences , , when
and are supported on intervals on the real line and their
Radon-Nikodym derivatives with respect to the arcsine distribution of the
respective interval are holomorphic functions
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