International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 5, Pages 335-344
doi:10.1155/S0161171200003616
On rational approximation in a ball in ℂN
P.W. Darko
, S.M. Einstein-Matthews
and C.H. Lutterodt
Department of Mathematics, Howard University, 2441 6th Street, N. W. Washington D. C 20059, USA
Abstract
We study rational approximations of elements of a special class of meromorphic functions which are characterized by their holomorphic behavior near the origin in balls in ℂN by means of their rational approximants. We examine two modes of convergence for this class: almost uniform-type convergence analogous to Montessus-type convergence and weaker form of convergence using capacity based on the classical Tchebychev constant. These methods enable us to generalize and extend key results of Pommeranke and Gonchar.