Geodesic
On the convergence of generalized Padé approximants of meromorphic functions
Sbornik. Mathematics, Tome 27 (1975) no. 4, pp. 503-514 
A. A. Gonchar. On the convergence of generalized Padé approximants of meromorphic functions. Sbornik. Mathematics, Tome 27 (1975) no. 4, pp. 503-514. http://geodesic.mathdoc.fr/item/SM_1975_27_4_a3/
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     title = {On~the convergence of generalized {Pad\'e} approximants of meromorphic functions},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The paper considers questions of the convergence of interpolating sequences of rational functions with partly free poles. Bibliography: 16 titles.

[1] J. Hadamard, “Essai sur L'étude des foncitions données par leur développement de Taylor”, J. Math. (4), 8 (1892), 101–186

[2] R. de Montessus de Ballore, “Sur les fractions continues algébriques”, Bull. Soc. Math. France, 30 (1902), 28–36 | MR | Zbl

[3] H. Wallin, “On the convergence theory of Pade approximants”, Linear Operators and Approximation, Proc. of a conference in Oberwolfach 1971, Birkhäuser, Stuttgart, 1972, 461–469 | MR

[4] H. Wallin, The convergence of Pade approximants and the size of the power series coefficients, preprint, University of Umeä

[5] J. Nuttall, “The convergence of Padé approximants, of meromorphic functions”, J. Math. Anal. Appl., 31 (1970), 147–153 | DOI | MR

[6] Ch. Pommerenke, “Padé approximants and convergence in capacity”, J. Math. Anal. Appl., 41 (1973), 775–780 | DOI | MR | Zbl

[7] A. A. Gonchar, “O skhodimosti approksimatsii Pade”, Matem. sb., 92(134):1(9) (1973), 152–164 | MR | Zbl

[8] A. A. Gonchar, “O skhodimosti approksimatsii Pade dlya nekotorykh klassov meromorfnykh funktsii”, Matem. sb., 97(139):4(8) (1975), 607–629 | MR | Zbl

[9] O. Perron, The Lehre von den Kettenbrüchen, Band II, Teubner, Stuttgart, 1957 | MR | Zbl

[10] H. S. Wall, Analytic theory of continued fractions, Van Nostrand, New York, 1948 | MR | Zbl

[11] Dzh. L. Uolsh, Interpolyatsiya i approksimatsiya ratsionalnymi funktsiyami v kompleksnoi oblasti, IL, Moskva, 1961 | MR

[12] V. I. Smirnov, N. A. Lebedev, Konstruktivnaya teoriya funktsii kompleksnogo peremennogo, izd-vo «Nauka», Moskva–Leningrad, 1964 | MR | Zbl

[13] N. S. Landkof, Osnovy sovremennoi teorii potentsiala, izd-vo «Nauka», Moskva, 1966 | MR

[14] G. M. Goluzin, Geometricheskaya teoriya funktsii kompleksnogo peremennogo, izd-vo «Nauka», Moskva, 1966 | MR

[15] E. B. Saff, “An extension of Montessus de Ballore's theorem on the convergence of interpolating rational functions”, J. Approximation Theory, 6 (1972), 63–68 | DOI | MR

[16] T. Bagby, “On interpolation by rational functions”, Duke Math. J., 36:1 (1969), 95–104 | DOI | MR | Zbl