Geodesic
Convergence of diagonal Padé approximants
Sbornik. Mathematics, Tome 33 (1977) no. 2, pp. 243-260 
E. A. Rakhmanov. Convergence of diagonal Padé approximants. Sbornik. Mathematics, Tome 33 (1977) no. 2, pp. 243-260. http://geodesic.mathdoc.fr/item/SM_1977_33_2_a4/
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     author = {E. A. Rakhmanov},
     title = {Convergence of diagonal {Pad\'e} approximants},
     journal = {Sbornik. Mathematics},
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     year = {1977},
     volume = {33},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1977_33_2_a4/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\mu$ be a positive measure with compact support contained in $\mathbf R$, and set $$ \widehat\mu(z)=\int(z-x)^{-1}\,d\mu(x). $$ This paper studies the convergence of diagonal Padé approximants for meromorphic functions of the form $f(z)=\widehat\mu(z)+r(z)$, where $r(z)$ is a rational function. Bibliography: 6 titles.

[1] G. M. Goluzin, Geometricheskaya teoriya funktsii kompleksnogo peremennogo, Nauka, M., 1966 | MR

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

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

[4] E. A. Rakhmanov, “Ob asimptotike otnosheniya ortogonalnykh mnogochlenov”, Matem. sb., 103(145) (1977), 237–252 | Zbl

[5] G. Sege, Ortogonalnye mnogochleny, Fizmatgiz, M., 1962

[6] H. Widom, “Extremal polinomials associated with a sistem of curves in the complex plane”, Adv. Math., 3:2 (1969), 127–232 | DOI | MR | Zbl