On the degree of rational approximation of meromorphic functions
Sbornik. Mathematics, Tome 81 (1995) no. 1, pp. 1-20 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Questions concerning the theory of rational approximation of analytic functions are considered. One of the main results is Theorem 1, which characterizes the degree of rational approximation of meromorphic functions of finite order. The proof of the results obtained are based on the methods of the theory of Hankel operators.
@article{SM_1995_81_1_a0,
     author = {V. A. Prokhorov},
     title = {On the degree of rational approximation of meromorphic functions},
     journal = {Sbornik. Mathematics},
     pages = {1--20},
     year = {1995},
     volume = {81},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_81_1_a0/}
}
TY  - JOUR
AU  - V. A. Prokhorov
TI  - On the degree of rational approximation of meromorphic functions
JO  - Sbornik. Mathematics
PY  - 1995
SP  - 1
EP  - 20
VL  - 81
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1995_81_1_a0/
LA  - en
ID  - SM_1995_81_1_a0
ER  - 
%0 Journal Article
%A V. A. Prokhorov
%T On the degree of rational approximation of meromorphic functions
%J Sbornik. Mathematics
%D 1995
%P 1-20
%V 81
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1995_81_1_a0/
%G en
%F SM_1995_81_1_a0
V. A. Prokhorov. On the degree of rational approximation of meromorphic functions. Sbornik. Mathematics, Tome 81 (1995) no. 1, pp. 1-20. http://geodesic.mathdoc.fr/item/SM_1995_81_1_a0/

[1] Gonchar A. A., Rakhmanov E. A., “Ravnovesnaya mera i raspredelenie nulei ekstremalnykh mnogochlenov”, Matem. sb., 125 (167) (1984), 117–127 | MR

[2] Gonchar A. A., Rakhmanov E. A., “Ravnovesnye raspredeleniya i skorost ratsionalnoi approksimatsii analiticheskikh funktsii”, Matem. sb., 134 (176) (1987), 306–352 | MR | Zbl

[3] Stahl H., “Orthogonal polynomials with complex valued weight function. I; II”, Constr. approx., 2 (1986), 225–240 ; 241–251 | DOI | MR | Zbl

[4] Nuttall J., “Asymptotics of diagonal Hermite–Padé polynomials”, J. Approx. Theory, 42 (1984), 299–386 | DOI | MR | Zbl

[5] Nuttall J., “Sets of minimal capacity, Padé approximants and bubble problem”, Bifurcation phenomena in Mathematical physics and related topics, eds. C. Bardos, D. Bessis, Reidel, Dordrecht, 1980, 185–201 | MR | Zbl

[6] Gonchar A. A., “O skorosti ratsionalnoi approksimatsii nekotorykh analiticheskikh funktsii”, Matem. sb., 105 (147) (1978), 147–163 | MR | Zbl

[7] Gonchar A. A., “O skorosti ratsionalnoi approksimatsii analiticheskikh funktsii”, Tr. MIAN, 166, Nauka, M., 1984, 52–60 | MR | Zbl

[8] Gonchar A. A., “Ratsionalnye approksimatsii analiticheskikh funktsii”, Tr. mezhdunarodnogo kongressa matematikov (Berkli, 1986), 1987

[9] Adamyan V. M., Arov D. Z., Krein M. G., “Analiticheskie svoistva par Shmidta, gankelevy operatory i obobschennaya zadacha Shura–Tagaki”, Matem. sb., 86 (128) (1971), 34–75 | MR

[10] Prokhorov V. A., “Ob odnoi teoreme Adamyana–Arova–Kreina”, Matem. sb., 184:1 (1993), 89–104 | MR | Zbl

[11] Parfenov O. G., “Otsenki singulyarnykh chisel operatora Karlesona”, Matem. sb., 131 (173) (1986), 501–518

[12] Peller V. V., Khruschev S. V., “Operatory Gankelya, nailuchshie priblizheniya i standartnye gaussovskie protsessy”, UMN, 37:1 (1982), 53–124 | MR | Zbl

[13] Peller V. V., “Opisanie operatorov Gankelya klassa $\sigma _p$ pri $p>0$, issledovanie skorosti ratsionalnoi approksimatsii i drugie prilozheniya”, Matem. sb., 122 (164) (1983), 481–510 | MR

[14] Prokhorov V. A., “Ratsionalnaya approksimatsiya analiticheskikh funktsii”, Matem. sb., 184:2 (1993), 3–32 | Zbl

[15] Nuttall J., “The convergence of Padé approximants of meromorphic functions”, J. Math. Anal. Appl., 31 (1970), 147–153 | DOI | MR

[16] Pommerenke C., “Padé approximants and convergence in capacity”, J. Math. Anal. Appl., 41 (1973), 775–780 | DOI | MR | Zbl

[17] Karlsson J., “Rational interpolation and best rational approximation”, J. Math. Appl., 53 (1976), 38–52 | DOI | MR | Zbl

[18] Edrei A., “Sur les déterminants récurrents et les singularités d'une fonction donnée par son développement de Taylor”, Comp. math., 7 (1939), 20–88 | MR | Zbl

[19] Shah S. M., “Polynomial approximation of an entire function and generalized order”, J. Approx. Theory, 19 (1977), 315–324 | DOI | MR | Zbl

[20] Sheremeta M. N., “O svyazi mezhdu rostom maksimuma modulya tseloi funktsii i modulyami koeffitsientov ee stepennogo razlozheniya”, Izv. vuzov. matem., 1967, no. 2, 100–108 | MR | Zbl

[21] Sheremeta M. N., “O svyazi mezhdu rostom tselykh i analiticheskikh v kruge funktsii nulevogo poryadka i koeffitsientami ikh stepennykh razlozhenii”, Izv. vuzov. matem., 1968, no. 6, 115–121 | MR | Zbl

[22] Kusis P., Vvedenie v teoriyu prostranstv $H^p$, Mir, M., 1984 | MR

[23] Privalov I. I., Granichnye svoistva analiticheskikh funktsii, Gostekhizdat, M.–L., 1950

[24] Tumarkin G. Ts., Khavinson S. Yu., “K opredeleniyu analiticheskikh funktsii klassa $E_p$ v mnogosvyaznykh oblastyakh”, UMN, 13:1 (1958), 201–206 | MR | Zbl

[25] Gokhberg I. Ts., Krein M. G., Vvedenie v teoriyu nesamosopryazhennykh operatorov v gilbertovom prostranstve, Nauka, M., 1976

[26] Kheiman U., Meromorfnye funktsii, Mir, M., 1966 | MR

[27] Markushevich A. I., Teoriya analiticheskikh funktsii, T. 2, Nauka, M., 1968 | Zbl

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

[29] Uolsh Dzh. L., Interpolyatsiya i approksimatsiya ratsionalnymi funktsiyami v kompleksnoi oblasti, IL, M., 1961 | MR