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A generalization of the classical Montessus de Ballore theorem in ℂn and some related theorems are discussed. Non-Montessus type of convergence in ℝ2n dimensional Lebesgue measure is presented linking it to a result of Gonĉar

international journal of mathematics and mathematical sciences

On convergence of<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>-sequences of unisolvent rational approximants to meromorphic functions in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$C^n $" id="E2"><mml:msup><mml:mi>C</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:math>

On convergence of(μ,ν)-sequences of unisolvent rational approximants to meromorphic functions inCn