International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 4, Pages 655-660
doi:10.1155/S0161171281000495

On uniform convergence for (μ,ν)-type rational approximants in ℂn-II

Abstract

This paper shows that if f(z) is analytic in some neighborhood of the origin, but meromorphic in ℂn otherwise, with a denumerable non-accumulating pole sections in ℂn and if for each fixed ν the pole set of each (μ,ν) unisolvent rational approximant πμν(z) tends to infinity as μ′=mini≤n(μi)→∞, then f(z) must be entire in ℂn. This paper also shows a monotonicity property for the “error sequence” eμν=‖f(z)−πμν(z)‖K on compact subsets K of  ℂn.