Geodesic
On a~lower bound for the rate of convergence of multipoint Pad\' e approximants of piecewise analytic functions
Izvestiya. Mathematics , Tome 85 (2021) no. 3, pp. 351-366

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We obtain a lower bound for the rate of convergence of multipoint Padé approximants of functions holomorphically extendable from a compact set to a union of domains whose boundaries possess a symmetry property. The bound obtained matches a known upper bound for the same quantity.
Keywords: rational approximation, convergence in capacity.
Mots-clés : orthogonal polynomials, Padé approximants, distribution of poles 
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     author = {V. I. Buslaev},
     title = {On a~lower bound for the rate of convergence of multipoint {Pad\'} e approximants of piecewise analytic functions},
     journal = {Izvestiya. Mathematics },
     pages = {351--366},
     publisher = {mathdoc},
     volume = {85},
     number = {3},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2021_85_3_a2/}
}
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V. I. Buslaev. On a~lower bound for the rate of convergence of multipoint Pad\' e approximants of piecewise analytic functions. Izvestiya. Mathematics , Tome 85 (2021) no. 3, pp. 351-366. http://geodesic.mathdoc.fr/item/IM2_2021_85_3_a2/