Convergence in measure of multivariate Pade approximants

Abstract

Convergence conclusions of Pade approximants in the univariate case can be found in various papers. However, results in the multivariate case are few. A. Cuyt seems to be the only one who discusses convergence for multivariate Pade approximants, she gives in [2] a de Montessus de Bollore type theorem. In this paper, we will discuss the zero set of a real multivariate polynomial, and present a convergence theorem in measure of multivariate Pade approximant. The proof technique used in this paper is quite different from that used in the univariate case.