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
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Received 3 June 1980
Copyright © 1981 Clement H. Lutterodt. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.