Geodesic
The rate of rational approximation and the property of single-valuedness of an analytic function in the neighborhood of an isolated singular point
Sbornik. Mathematics, Tome 23 (1974) no. 2, pp. 254-270 Cet article a éte moissonné depuis la source Math-Net.Ru

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Criteria are obtained for the single-valuedness of an analytic function $\mathscr F$ in the neighborhood of an isolated singular point in terms of the rate of convergence of rational approximation to a fixed branch of the function $\mathscr F$. Bibliography: 8 titles. 
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A. A. Gonchar. The rate of rational approximation and the property of single-valuedness of an analytic function in the neighborhood of an isolated singular point. Sbornik. Mathematics, Tome 23 (1974) no. 2, pp. 254-270. http://geodesic.mathdoc.fr/item/SM_1974_23_2_a5/

[1] A. A. Gonchar, “Lokalnoe uslovie odnoznachnosti analiticheskikh funktsii”, Matem. sb., 89(131) (1972), 148–164 | Zbl

[2] W. I. Cody, G. Meinardus, R. S. Varda, “Chebyshev rational approximations to $e^{-x}$ in $[0, \infty]$ and applications to heat-conduction problems”, J. approximation theory, 2:1 (1969), 50–65 | DOI | MR | Zbl

[3] A. A. Gonchar, “O skorosti ratsionalnoi approksimatsii nepreryvnykh funktsii s kharakternymi osobennostyami”, Matem. sb., 73(115) (1967), 630–638 | Zbl

[4] G. Polia, G. Sege, Izoperimetricheskie neravenstva v matematicheskoi fizike, Fizmatgiz, Moskva, 1962 | MR

[5] T. Bagby, “The modulus of a plane condenser”, J. Math. and Mech., 17:4 (1967), 315–329 | MR | Zbl

[6] A. A. Gonchar, “O zadachakh E. I. Zolotareva, svyazannykh s ratsionalnymi funktsiyami”, Matem. sb., 78(120) (1968), 640–654

[7] A. A. Gonchar, “O skhodimosti approksimatsii Pade”, Matem. sb., 92(134) (1973), 152–164 | Zbl

[8] A. P. Bulanov, “Asimptotika dlya naimenshikh uklonenii $|x|$ ot ratsionalnykh funktsii”, Matem. sb., 76 (118) (1968), 288–303 | MR | Zbl