International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 4, Pages 655-660

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

Clement H. Lutterodt

6935 Spinning Seed Road, Columbia, Maryland 21045, USA

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.


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