Rational approximation of analytic functions
Sbornik. Mathematics, Tome 78 (1994) no. 1, pp. 139-164 Cet article a éte moissonné depuis la source Math-Net.Ru

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This article is devoted to results relating to the theory of rational approximation of analytic functions. An analysis is made of the rate of decrease of the best approximations $\rho_n$ of an analytic functions of order at most $n$ in the uniform metric in terms connected with the properties of the function to be approximated, more precisely, connected with the distribution and structure of its set of singularities and with the character of its analytic continuation.
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V. A. Prokhorov. Rational approximation of analytic functions. Sbornik. Mathematics, Tome 78 (1994) no. 1, pp. 139-164. http://geodesic.mathdoc.fr/item/SM_1994_78_1_a8/

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

[2] Bagby T., “On interpolation by rational functions”, Duke Math. J., 36 (1969), 95–104 | DOI | MR | Zbl

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

[4] Gonchar A. A., “Ratsionalnye approksimatsii analiticheskikh funktsii”, Trudy Mezhdunarodnogo kongressa matematikov (Berkli, 1986), 1987

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

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

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

[8] Nutall J., “Asymptotics of diagonal Hermite-Pade polynomials”, J. Appr. Theory, 42:4 (1984), 299–386 | DOI | MR

[9] Nutall J., “Sets of minimal capacity, Pade approximations and bubble problem”, Bifurcation phenomena in Mathematical physics and related topics, eds. C. Bardos, D. Bessis, Reidel, Dordrecht, 1980, 185–201

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

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

[12] Peller V. V., “Operatory Gankelya klassa $\sigma _p$ i ikh prilozheniya”, Matem. sb., 113 (157) (1980), 538–581 | MR | Zbl

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

[14] 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

[15] Gonchar A. A., “Rational approximation of analytic functions”, Linear and complex analysis problems, Lect. Notes Math., 1043, eds. V. P. Havin, S. V. Hruscev, N. K. Nikol'sci, Springer, 1982, 471–474

[16] 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

[17] Prokhorov V. A., O skorosti ratsionalnoi approksimatsii analiticheskikh funktsii, Preprint VINITI. 313-V92, Belorus. un-t, 1991

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

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

[20] Gonchar A. A., “Lokalnoe uslovie odnoznachnosti analiticheskikh funktsii”, Matem. sb., 89(131) (1972), 148–164 | MR | Zbl

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

[22] Privalov I. I., Granichnye svoistva analiticheskikh funktsii, Gostekhizdat, M.-L., 1950

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

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

[25] Garnet Dzh., Ogranichennye analiticheskie funktsii, Mir, M., 1984 | MR | Zbl

[26] Landkof N. S., Osnovy sovremennoi teorii potentsiala, Nauka, M., 1966 | MR | Zbl

[27] Tsuji M., Potential Theory in Modern Functions Theory, Maruzen, Tokyo, 1959 | MR | Zbl

[28] Varga R. S., “On an extension of a result of S. N. Bernstein”, J. Approx. Theory, 1 (1968), 176–179 | DOI | MR | Zbl

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

[30] Winiarski T., “Approximation and interpolation of entire functions”, Ann. Polon. Math., 23 (1970), 259–273 | MR | Zbl

[31] Polya G., “Beitrag zur Verallgemeinerung des Verzerrungssatzes auf mehrfach zusammenhängende Gebiete, III”, Sitzgsber Preuss. Acad. Wiss. Phys.-Math. Kl., 1929, 55–62 | Zbl