On Overconvergence of Closed to Row Subsequences of Classical Pade Approximants

摘要

Let f (z) := Sigma f(nu)z(nu) be a power series with positive radius of convergence. In the present paper, we study the phenomenon of overconvergence of sequences of classical Pade approximants {pi(n),m(n)} associated with f, where m(n) -> 8, m(n) <= m(n+1) <= m(n) + 1 and m(n) = o(n/ log n), resp. mn = o(n) as n -> 8. We extend classical results by J. Hadamard and A. A. Ostrowski related to overconvergent Taylor polynomials, as well as results by G. Lopez Lagomasino and A. Fernandes Infante concerning overconvergent subsequences of a fixed row of the Pade table.