On the convergence of the Padé approximants for meromorphic functions of Stieltjes type
Sbornik. Mathematics, Tome 39 (1981) no. 2, pp. 281-288 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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.
@article{SM_1981_39_2_a8,
     author = {G. L. Lopes},
     title = {On the convergence of the {Pad\'e} approximants for meromorphic functions of {Stieltjes} type},
     journal = {Sbornik. Mathematics},
     pages = {281--288},
     year = {1981},
     volume = {39},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1981_39_2_a8/}
}
TY  - JOUR
AU  - G. L. Lopes
TI  - On the convergence of the Padé approximants for meromorphic functions of Stieltjes type
JO  - Sbornik. Mathematics
PY  - 1981
SP  - 281
EP  - 288
VL  - 39
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1981_39_2_a8/
LA  - en
ID  - SM_1981_39_2_a8
ER  - 
%0 Journal Article
%A G. L. Lopes
%T On the convergence of the Padé approximants for meromorphic functions of Stieltjes type
%J Sbornik. Mathematics
%D 1981
%P 281-288
%V 39
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1981_39_2_a8/
%G en
%F SM_1981_39_2_a8
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/

[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