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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

international journal of mathematics and mathematical sciences

On uniform convergence for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$\left( {\mu ,\nu } \right)$" id="E1"><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>μ</mml:mi><mml:mo>,</mml:mo><mml:mi>ν</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>-type rational approximants in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$\mathbb{C}^n $" id="E2"><mml:msup><mml:mi>ℂ</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:math>-II

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