Convergence in Hausdorff Content of Generalized Simultaneous Pade Approximants

Methawee Wajasat, Nattapong Bosuwan

Abstract

Given a vector of the approximated functions analytic on a neighborhood of some compact subset of the complex plane with simply connected complement in the extended complex plane, we prove convergences in Hausdorff content of the corresponding two generalizations of type II Hermite-Pade approximants on some certain sequences. These two generalizations are based on orthogonal and Faber polynomial expansions. As consequences of these convergence results, we give alternate proofs of Montessus de Ballore type theorems for these generalizations.