Geodesic
Conditions for convergence of multipoint Padé approximants for functions of Stieltjes type
Sbornik. Mathematics, Tome 35 (1979) no. 3, pp. 363-376 
G. López Lagomasino. Conditions for convergence of multipoint Padé approximants for functions of Stieltjes type. Sbornik. Mathematics, Tome 35 (1979) no. 3, pp. 363-376. http://geodesic.mathdoc.fr/item/SM_1979_35_3_a4/
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     title = {Conditions for convergence of multipoint {Pad\'e} approximants for functions of {Stieltjes} type},
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     url = {http://geodesic.mathdoc.fr/item/SM_1979_35_3_a4/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A sufficient condition for the convergence of multipoint Padé approximants for functions of Stieltjes type is given. Bibliography: 12 titles.

[1] A. A. Markov, Izbrannye trudy po teorii nepreryvnykh drobei i teorii funktsii, naimenee uklonyayuschiesya ot nulya, Gostekhizdat, Moskva, 1948

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

[3] T. Stiltes, Issledovanie o nepreryvnykh drobyakh, ONTI, Kharkov–Kiev, 1936

[4] T. Carleman, Les fonctions quasi-analytiques, Paris, 1926

[5] M. Barnsley, “The bounding properties of the multipoint appoximant to a series of Stieltjes on the real line”, J. Math. Phys., 14:3 (1973), 299–313 | DOI | MR | Zbl

[6] A. A. Gonchar, G. Lopes, “O teoreme Markova dlya mnogotochechnykh approksimatsii Pade”, Matem. sb., 105(147) (1978), 512–524 | MR | Zbl

[7] J. Karlsson, “Rational interpolation and best rational appoximation”, J. Math. Anal. Appl., 53:1 (1976), 38–51 | DOI | MR

[8] G. Lopes, “O skhodimosti mnogotochechnykh approksimatsii Pade dlya funktsii stiltesovskogo tipa”, DAN SSSR, 239:4 (1978), 793–796 | MR

[9] P. L. Duren, Theory of $H^p$ Spaces, New York–London, Acad. Press, 1970 | MR | Zbl

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

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

[12] M. G. Krein, A. A. Nudelman, Problema momentov Markova i ekstremalnye zadachi, izd-vo “Nauka”, Moskva, 1973 | MR