On rational approximation in a ball in ℂ N

P. W. Darko, S. M. Einstein-Matthews and C. H. Lutterodt

International Journal of Mathematics and Mathematical Sciences, 2000, vol. 24, 1-10

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 ℂ N 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.

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:389423

DOI: 10.1155/S0161171200003616

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