Geodesic
Convergence of $m$-point Pad\'e approximants of a~tuple of multivalued analytic functions
Sbornik. Mathematics, Tome 206 (2015) no. 2, pp. 175-200

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We prove the convergence of $m$-point Padé approximants of an $m$-tuple of holomorphic germs that admit analytic continuation along all paths in the extended complex plane that do not pass through a finite set of points. This result extends Stahl's theorem from the case $m=1$ to the case of an arbitrary $m\in\mathbb N$. Bibliography: 15 titles.
Keywords: rational approximation, convergence in capacity, limiting distribution of poles.
Mots-clés : orthogonal polynomials, Padé approximants 
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     author = {V. I. Buslaev},
     title = {Convergence of $m$-point {Pad\'e} approximants of a~tuple of multivalued analytic functions},
     journal = {Sbornik. Mathematics},
     pages = {175--200},
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     volume = {206},
     number = {2},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2015_206_2_a0/}
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V. I. Buslaev. Convergence of $m$-point Pad\'e approximants of a~tuple of multivalued analytic functions. Sbornik. Mathematics, Tome 206 (2015) no. 2, pp. 175-200. http://geodesic.mathdoc.fr/item/SM_2015_206_2_a0/