Geodesic
On the convergence of the Padé approximants for meromorphic functions of Stieltjes type
Sbornik. Mathematics, Tome 39 (1981) no. 2, pp. 281-288 
G. L. Lopes. On the convergence of the Padé approximants for meromorphic functions of Stieltjes type. Sbornik. Mathematics, Tome 39 (1981) no. 2, pp. 281-288. http://geodesic.mathdoc.fr/item/SM_1981_39_2_a8/
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     title = {On the convergence of the {Pad\'e} approximants for meromorphic functions of {Stieltjes} type},
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     volume = {39},
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     url = {http://geodesic.mathdoc.fr/item/SM_1981_39_2_a8/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The convergence problem is studied for the diagonal Padé approximants for functions of the form $f=\widehat\mu+r$, where $\mu$ is a positive measure on $[0,+\infty)$, $\widehat\mu=\mu*\frac1z$ and $r$ is a rational function with real coefficients. Bibliography: 12 titles.

[1] O. Perron, Die Lehre von den Kettenbruchen, Band II, Teubner, Stuttgart, 1957 | MR | Zbl

[2] H. S. Wall, Analytic Theory of Continued Fractions, Van Nostrand, New York, 1948 | MR | Zbl

[3] A. A. Markov, Izbrannye trudy po teorii nepreryvnykh drobei i teorii funktsii, naimenee uklonyayuschikhsya ot nulya, Gostekhizdat, Moskva, 1948 | MR

[4] T. Stiltes, Issledovaniya o nepreryvnykh drobyakh, ONTI, Kharkov–Kiev, 1936

[5] T. Carleman, Les fonctions quasi-analytique, Paris, 1926

[6] A. A. Gonchar, “O skhodimosti approksimatsii Pade dlya nekotorykh klassov meromorfnykh funktsii”, Matem. sb., 97(139) (1975), 608–629

[7] E. A. Rakhmanov, “O skhodimosti diagonalnykh approksimatsii Pade”, Matem. sb., 104(146) (1977), 271–291 | Zbl

[8] G. Sege, Ortogonalnye mnogochleny, Fizmatgiz, Moskva, 1962

[9] G. M. Goluzin, Geometricheskaya teoriya funktsii kompleksnogo peremennogo, izd-vo “Nauka”, Moskva, 1966 | MR

[10] A. A. Gonchar, “O skhodimosti obobschennykh approksimatsii Pade meromorfnykh funktsii”, Matem. sb., 98(140) (1975), 564–577 | Zbl

[11] A. A. Gonchar, Giermo Lopes L., “O teoreme Markova dlya mnogotochechnykh approksimatsii Pade”, Matem. sb., 105(147) (1978), 513–524 | MR

[12] G. Lopes, “Usloviya skhodimosti mnogotochechnykh approksimatsii Pade dlya funktsii stiltesovskogo tipa”, Matem. sb., 107(149) (1978), 60–83 | MR