On rational approximation in a ball in ℂN

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.

Keywords

• Rational approximation
• meromorphic functions
• Montessus-type convergence
• weak convergence in capacity
• Tchebychev constant
• unisolvent rational approximation (URA)-sequences.