Geodesic
On an inverse problem for the $m$th row of a Padé table
Sbornik. Mathematics, Tome 52 (1985) no. 1, pp. 231-244 
S. P. Suetin. On an inverse problem for the $m$th row of a Padé table. Sbornik. Mathematics, Tome 52 (1985) no. 1, pp. 231-244. http://geodesic.mathdoc.fr/item/SM_1985_52_1_a12/
@article{SM_1985_52_1_a12,
     author = {S. P. Suetin},
     title = {On an inverse problem for the $m$th row of a {Pad\'e} table},
     journal = {Sbornik. Mathematics},
     pages = {231--244},
     year = {1985},
     volume = {52},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1985_52_1_a12/}
}
TY  - JOUR
AU  - S. P. Suetin
TI  - On an inverse problem for the $m$th row of a Padé table
JO  - Sbornik. Mathematics
PY  - 1985
SP  - 231
EP  - 244
VL  - 52
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1985_52_1_a12/
LA  - en
ID  - SM_1985_52_1_a12
ER  - 
%0 Journal Article
%A S. P. Suetin
%T On an inverse problem for the $m$th row of a Padé table
%J Sbornik. Mathematics
%D 1985
%P 231-244
%V 52
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1985_52_1_a12/
%G en
%F SM_1985_52_1_a12

Voir la notice de l'article provenant de la source Math-Net.Ru

The author considers the connection between the asymptotic behavior of the poles of the $m$th row of the Padé table of a function given by a power series and the singular points of this function on the boundary of its $m$th disc of meromorphicity. Bibliography: 9 titles.

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

[2] Gonchar A. A., “Polyusy strok tablitsy Pade i meromorfnoe prodolzhenie funktsii”, Matem. sb., 115(157) (1981), 590–613 | MR | Zbl

[3] Suetin S. P., “O polyusakh $m$-i stroki tablitsy Pade”, Matem. sb., 120(162) (1983), 500–504 | MR | Zbl

[4] Vavilov V. V., Lopes G., Prokhorov V. A., “Ob odnoi obratnoi zadache dlya strok tablitsy Pade”, Matem. sb., 110(152) (1979), 117–129. | MR

[5] Biberbakh L., Analiticheskoe prodolzhenie, Nauka, M., 1967 | MR

[6] Vavilov V. V., “Ob osobykh tochkakh meromorfnoi funktsii, zadannoi svoim ryadom Teilora”, DAN SSSR, 231:6 (1976), 1281–1284 | MR | Zbl

[7] Agmon S., “Sur les series de Dirichlet”, Ann. Ec. Norm. Sup., 66 (1949), 263–310 | MR | Zbl

[8] Vavilov V. V., Prokhorov V. A., Suetin S. P., “Polyusy $m$-i stroki tablitsy Pade i osobye tochki funktsii”, Matem. sb., 122(164) (1983), 475–480. | MR | Zbl

[9] Mandelbroit S., Ryady Dirikhle. Printsipy i metody, Mir, M., 1973 | Zbl