A multivariate convergence theorem of the “de Montessus de Ballore” type
Journal of Computational and Applied Mathematics - Special issue on extrapolation and rational approximation
Journal of Computational and Applied Mathematics
Multivariate partial Newton-Pade´ and Newton-Pade´ type approximants
Journal of Approximation Theory
A direct approach to convergence of multivariate, nonhomogeneous, Pade´ approximants
Journal of Computational and Applied Mathematics
Nuttall-Pommerenke theorems for homogeneous Pade´ approximants
Journal of Computational and Applied Mathematics
On the convergence of general order multivariate Pade´-type approximants
Journal of Approximation Theory
Convergence of the nested multivariate Pade´ approximants
Journal of Approximation Theory
Generalized multivariate Pade´ approximants
Journal of Approximation Theory
On rational interpolation to meromorphic functions in several variables
Journal of Approximation Theory
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
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In a previous paper, the author introduced a new class of multivariate rational interpolants, which are called Optimal Pade-type Approximants (OPTA). There, for this class of rational interpolants, which extends classical univariate Pade Approximants, a direct extension of the ''de Montessus de Ballore's Theorem'' for meromorphic functions in several variables is established. In the univariate case, this theorem ensures uniform convergence of a row of Pade Approximants when the denominator degree equals the number of poles (counting multiplicities) in a certain disc. When one overshoots the number of poles when fixing the denominator degree, convergence in measure or capacity has been proved and, under certain additional restrictions, the uniform convergence of a subsequence of the row. The author tackles the latter case and studies its generalization to functions in several variables by using OPTA.