Convergence of multipoint Padé approximants of piecewise analytic functions

The behaviour as $n\to\infty$ of multipoint Padé approximants to a function which is (piecewise) holomorphic on a union of finitely many continua is investigated. The convergence of multipoint Padé approximants is proved for a function which extends holomorphically from these continua to a union of domains whose boundaries have a certain symmetry property. An analogue of Stahl's theorem is established for two-point Padé approximants to a pair of functions, either of which is a multivalued analytic function with finitely many branch points.
Bibliography: 11 titles.