Geodesic
Convergence of multipoint Pad\'e approximants of piecewise analytic functions
Sbornik. Mathematics, Tome 204 (2013) no. 2, pp. 190-222

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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.
Keywords: rational approximation, convergence in capacity, asymptotic behaviour of poles.
Mots-clés : orthogonal polynomials, Padé approximants 
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     author = {V. I. Buslaev},
     title = {Convergence of multipoint {Pad\'e} approximants of piecewise analytic functions},
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     volume = {204},
     number = {2},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2013_204_2_a2/}
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V. I. Buslaev. Convergence of multipoint Pad\'e approximants of piecewise analytic functions. Sbornik. Mathematics, Tome 204 (2013) no. 2, pp. 190-222. http://geodesic.mathdoc.fr/item/SM_2013_204_2_a2/