Geodesic
On simultaneous Padé approximants
Sbornik. Mathematics, Tome 41 (1982) no. 4, pp. 409-425 
E. M. Nikishin. On simultaneous Padé approximants. Sbornik. Mathematics, Tome 41 (1982) no. 4, pp. 409-425. http://geodesic.mathdoc.fr/item/SM_1982_41_4_a0/
@article{SM_1982_41_4_a0,
     author = {E. M. Nikishin},
     title = {On simultaneous {Pad\'e} approximants},
     journal = {Sbornik. Mathematics},
     pages = {409--425},
     year = {1982},
     volume = {41},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1982_41_4_a0/}
}
TY  - JOUR
AU  - E. M. Nikishin
TI  - On simultaneous Padé approximants
JO  - Sbornik. Mathematics
PY  - 1982
SP  - 409
EP  - 425
VL  - 41
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SM_1982_41_4_a0/
LA  - en
ID  - SM_1982_41_4_a0
ER  - 
%0 Journal Article
%A E. M. Nikishin
%T On simultaneous Padé approximants
%J Sbornik. Mathematics
%D 1982
%P 409-425
%V 41
%N 4
%U http://geodesic.mathdoc.fr/item/SM_1982_41_4_a0/
%G en
%F SM_1982_41_4_a0

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

A rather large class of systems of functions is investigated in connection with the simultaneous Padé approximants (normality, perfectness, problems of uniform convergence). Bibliography: 20 titles.

[1] K. Mahler, “Perfect systems”, Compositio Math., 19 (1968), 95–166 | MR | Zbl

[2] C. Hermite, “Sur la fonction exponentielle”, Oeuvres, III (1873), 151–181

[3] P. L. Chebyshev, Polnoe sobr. soch., t. 3, Izd. AN SSSR, Moskva, 1948

[4] A. A. Markov, Izbrannye trudy o nepreryvnykh drobyakh i teorii funktsii, naimenee uklonyayuschikhsya ot nulya, Gostekhizdat, Moskva, 1948

[5] T. Stieltjes, “Recherches sur les fractions continues”, Ann. de Toulouse, VIII-IX (1894–1895) | MR | Zbl

[6] J. Coates, “On the algebraic approximation of functions. I, II, III”, Indag. Math., 28 (1966), 421–434 ; 435–448 ; 449–461 | MR | Zbl

[7] H. Jager, “A multidimensional generalization of the Padé table”, Indag. Math., 26 (1964), 192–249

[8] M. G. de Bruin, Threé new examples of generalized Padé tables which are partly normal, Depart of Math., Univ. Amsterdam, report 76–11 | Zbl

[9] M. G. de Bruin, “Convergence in the Padé table for ${}_1F_1(1,c;x)$”, Indag. Math., 79 (1976) | Zbl

[10] J. Nuttall, The Convergence of Padé Approximants for a Class of Functions with Branch Points (in manuscript)

[11] A. A. Gonchar, “O skhodimosti approksimatsii Pade dlya nekotorykh klassov meromorfnykh funktsii”, Matem. sb., 97(139):4(8) (1975), 607–629 | MR | Zbl

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

[13] M. A. Angelesko, “Sur deux extensions des fractions continues algebriques”, C. r. Acad. Sci. Paris, 168 (1919)

[14] E. M. Nikishin, “O sisteme markovskikh funktsii”, Vestnik MGU, matem. i mekhan., 1979, no. 4, 60–63 | MR | Zbl

[15] V. A. Kalyagin, “Ob odnom klasse polinomov, opredelyaemykh dvumya sootnosheniyami ortogonalnosti”, Matem. sb., 110(152) (1979), 609–627 | MR

[16] V. I. Parusnikov, “Algoritm Yakobi–Perrona i sovmestnoe priblizhenie funktsii”, Matem. sb., 114(156):2 (1981), 322–333 | MR | Zbl

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

[18] A. O. Gelfond, Yu. V. Linnik, Elementarnye metody v analiticheskoi teorii chisel, Fizmatgiz, Moskva, 1962

[19] N. I. Akhiezer, Klassicheskaya problema momentov, Fizmatgiz, Moskva, 1961

[20] R. J. Arms, A. Edrei, “The Pade tables and continued fractions generated by totally positive sequences”, Math. Essays, Dedicated to A. J. Macintyre, Ohio Univ. Press, 1970, 1–21 | MR