Rate of convergence of row sequences of multipoint Padé approximants

摘要

As a consequence of studying the exact rate of convergence of row sequences of multipoint Padé approximants, we prove that their zero limit distribution is a generalized balayage measure determined by the table of interpolation points and the region of meromorphy of the function being approximated, provided the configuration of these sets satisfies mild topological restrictions. Should there exist a subsequence of approximants converging at a faster rate on a given continuum that does not reduce to a single point, we prove that such a subsequence is overconvergent in the sense of the Hausdorff content.