The uniform convergence of subsequences of the last intermediate row of the Pade table

摘要

in the work the uniform convergence of rows of the Pade approximants for a meromorphic function a(z) is studied. The complete description of the asymptotic behavior of denominators Q(n)(z) of the Pade approximants is obtained for the (lambda - 1)th row. Here lambda is the number of the poles of a(z). The limits of all convergent subsequences of {Q(n)(z)} are explicitly computed. These limits form a family of polynomials which is parametrized by a monothetic subgroup F of the torus T-nu. The group F is constructed via the arguments Theta(l),...,Theta(nu), of those poles of a(z) of the maximal modulus that have the maximal multiplicity. (C) 2003 Elsevier Science (USA). All rights reserved. [References: 32]