Convergence of Shafer quadratic approximants. (English. Russian original) Zbl 1350.41003

Russ. Math. Surv. 71, No. 2, 373-375 (2016); translation from Usp. Mat. Nauk 71, No. 2, 205-206 (2016).
V. I. Buslaev and S. P. Suetin [Proc. Steklov Inst. Math. 290, 256–263 (2015; Zbl 1335.31002); translation from Tr. Mat. Inst. Steklova 290, 272–279 (2015)], A. A. Gonchar et al. [ibid. 200, 149–159 (1993; Zbl 0790.41011)] and R. K. Kovacheva and S. P. Suetin [ibid. 284, 168–191 (2014; Zbl 1311.41011); translation from Tr. Mat. Inst. Steklova 284, 176–199 (2014)] proved that given a Nuttall condenser, a Riemann surface with three sheets can be constructed in a standard way and the abelian integral on this surface satisfies some relations. In this paper, authors considered three-sheeted Riemann surfaces for which the partition into sheets is realized using a Nuttall condenser and found that a single valued meromorphic function on this surface given by its germ at the point at infinity can be recovered from this germ on the first and second sheets and their common boundary with the help of Hermite-Pade polynomials.


41A05 Interpolation in approximation theory
30F99 Riemann surfaces
41A21 Padé approximation
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