[1] |
Bieberbach L., “Über die Koeffizienten derjenigen Potenzreihen welche eine schlichte Abbildung des Einheitskreises vermitteln, sitzungsber”, Preuss. Akad. Wiss. Phys. Math. Kl., 138 (1916), 940-955 · JFM 46.0552.01 |
[2] |
Löwner K., “Untersuchungen uber schlichte konforme Abbildung des Einheitskreises. I”, Math. Ann., 89 (1923), 103-121 · JFM 49.0714.01 · doi:10.1007/BF01448091 |
[3] |
Littlewood J.E., “On inequalities of the theory of functions”, Proc. London Math. Soc., 23 (1925), 481-519 · JFM 51.0247.03 · doi:10.1112/plms/s2-23.1.481 |
[4] |
Fekete S., “Eine Bemerkung uber ungerade Funktionen”, J. London Math. Soc., 8 (1933), 85-89 · Zbl 0006.35302 · doi:10.1112/jlms/s1-8.2.85 |
[5] |
Goluzin G.M., “O koeffitsientakh odnolistnykh funktsii”, Matem. sb., 22(64):3 (1948), 373-380 · Zbl 0036.18702 |
[6] |
Bazilevich I.E., “O teoremakh iskazheniya i koeffitsientakh odnolistnykh funktsii”, Matem. sb., 28(70):1 (1951), 147-164 · Zbl 0044.30801 |
[7] |
Garabedian P.R., Shiffer M.A., “A proof of the Bieberbach conjecture for the fourth coefficient”, J. Ration. Mech. Anal., 4 (1955), 427-465 · Zbl 0065.06902 |
[8] |
Milin M.M., “Otsenka koeffitsientov odnolistnykh funktsii”, DAN SSSR, 160:4 (1965), 769-771 · Zbl 0158.32201 |
[9] |
Pederson R.N., “A proof of the Bieberbach conjecture for the sixth coefficient”, Arch. Ration. Mech. and Anal., 31 (1968), 331-351 · Zbl 0184.10501 · doi:10.1007/BF00251415 |
[10] |
Ozawa M., “An elementary proof of the Bieberbach conjecture for the sixth coefficient”, Kodai Math. Semin. Repts., 21 (1969), 129-132 · Zbl 0202.07201 · doi:10.2996/kmj/1138845875 |
[11] |
Pederson R.N., Shiffer M.A., “A proof of the Bieberbach conjecture for the fifth coefficient”, Arch. Ration. Mech. and Anal., 45 (1972), 161-193 · Zbl 0241.30025 · doi:10.1007/BF00281531 |
[12] |
Fitzgerald C.H., “Exponentiation of certain quadratic inequalities for schlicht functions”, Bull. Amer. Math. Soc., 78 (1972), 209-210 · Zbl 0229.30020 · doi:10.1090/S0002-9904-1972-12919-7 |
[13] |
Horoviz D., “A refinement for coefficient estimates of univalent functions”, Proc. Amer. Math. Soc., 54 (1976), 176-178 · Zbl 0294.30006 · doi:10.1090/S0002-9939-1976-0396932-X |
[14] |
Lowner K., “Untersuchungen uber die Verzerrung bei konformen Abbildung des Einheitskreises \(|z|<1\), die durch Funktionen mit nicht verschwinden der Ableitung geliefert warden”, Leipziger Berichter, 69 (1917), 89-106 · JFM 46.0556.02 |
[15] |
Nevanlinna R., “Über die Konforme Abbildung von Sterngebieten”, Ofvers Finska Vet. Soc. Forh., 53(A):6 (1921) · JFM 48.0403.14 |
[16] |
Dieudonne, “Sur les functions univalentes”, C.R., 192 (1931), 1148-1150 · Zbl 0001.34401 |
[17] |
Kaplan W., “Close-to-convex schlicht functions”, Michigan Math. J., 1:2 (1952), 169-185 · Zbl 0048.31101 · doi:10.1307/mmj/1028988895 |
[18] |
Bazilevich I.E., “Oblasti nachalnykh koeffitsientov ogranichennykh odnolistnykh funktsii \(r\)-kratnoi simmetrii”, Matem. sb., 43:4 (1957), 409-428 · Zbl 0080.05801 |
[19] |
Kufarev P.P., “Odno zamechanie ob ekstremalnykh zadachakh teorii odnolistnykh funktsii”, Uchenye zapiski Tomskogo universiteta, 14 (1950), 3-4 |
[20] |
Kufarev P.P., “Ob odnom svoistve ekstremalnykh oblastei zadachi koeffitsientov”, DAN SSSR, 97:3 (1954), 391-393 · Zbl 0056.30001 |
[21] |
Kufarev P.P., “Odno zamechanie k zadache koeffitsientov”, Uchenye zapiski Tomskogo universiteta, 25 (1955), 15-18 |
[22] |
Kheiman K., Mnogolistnye funktsii, IL, M., 1960 |
[23] |
Milin I.M., Odnolistnye funktsii i ortonormirovannye sistemy, Nauka, M., 1971, 256 pp. · Zbl 0228.30011 |
[24] |
Bazilevich I.E., “O dispersii koeffitsientov odnolistnykh funktsii”, Matem. sb., 68(110):4 (1965), 549-560 · Zbl 0144.33401 |
[25] |
Shirokov N.A., “Teorema regulyarnosti Kheimana”, Zap. nauchn. semin. LOMI AN SSSR, 24, 1972, 182-200 · Zbl 0266.30018 |
[26] |
Lebedev N.A., Milin I.M., “Ob odnom neravenstve”, Vestnik Leningradskogo universiteta, 19 (1965), 157-158 · Zbl 0144.33303 |
[27] |
Milin I.M., “O koeffitsientakh odnolistnykh funktsii”, DAN SSSR, 176:5 (1967), 1015-1018 · Zbl 0176.03201 |
[28] |
Grinshpan A.Z., “Koeffitsienty neravenstva dlya konformnykh otobrazhenii s gomeomorfnym prodolzheniem”, Sibirskii matem. zhurnal, 26:1 (1985), 49-65 · Zbl 0569.30016 |
[29] |
Grinshpan A.Z., “Odnolistnye funktsii i regulyarno izmerimye otobrazheniya”, Sibirskii matem. zhurnal, 27:6 (1986), 50-64 · Zbl 0617.30016 |
[30] |
Fitzgerald C.N., “Quadratic inequalities and coefficient estimates for schlicht function”, Arch. Rational. Mech. and Anal., 46:5 (1972), 356-368 · Zbl 0242.30013 · doi:10.1007/BF00281102 |
[31] |
Milin I.M., Odnolistnye funktsii i ortonormirovannye sistemy, Nauka, M., 1971 · Zbl 0228.30011 |
[32] |
Branges L., A proof of the Bieberbach conjecture, LOMI preprintes, E. 5-84, 21 pp. |
[33] |
Aleksandrov I.A., “Dokazatelstvo L. de Branzha gipotezy I.M. Milina i gipotezy L. Biberbakha”, Sibirskii matem. zhurnal, 28:2 (1987), 7-20 · Zbl 0624.30024 |
[34] |
Aleksandrov I.A., Milin I.M., “O gipoteze Biberbakha i logarifmicheskikh koeffitsientakh odnolistnykh funktsii”, Izv. vuzov. Matematika, 1989, no. 8(327), 3-15 · Zbl 0693.30001 |
[35] |
Sadritdinova G.D., “Oblasti s razrezami i svoistva upravlyayuschikh funktsii v uravnenii Levnera”, Tez. dokl. Mezhdunar. konf. po matem. i mekhanike, TGU, Tomsk, 2003 |
[36] |
Yuferova G.A., “Uravnenie Levnera i ortogonalnye mnogochleny”, Vestnik TGU, 2007, no. 298, 121-124 |
[37] |
Aleksandrov I.A., Aleksandrov A.I., Kasatkina T.V., “Funktsional Milina i polinomy de Branzha”, Aktualnye problemy sovremennoi matematiki, 3, NII MIOO, Novosibirsk, 1997, 13-18 · Zbl 0915.30014 |
[38] |
Aleksandrov I.A., “Proizvodyaschaya funktsiya dlya polinomov de Branzha”, Teoriya funktsii i ee primeneniya, Tez. dokl. shkoly-konferentsii (15-22 iyunya 1995 g., g. Kazan), 1995, 4-6 |
[39] |
Weinstein L., “The Bieberbach conjecture”, Intern. Math. Res. Notices, 5 (1991), 61-64 · Zbl 0743.30021 · doi:10.1155/S1073792891000089 |
[40] |
Wilf H., “A footnote on two proof of the Bieberbach conjecture – de Branges Theorem”, Bull. London Math. Soc., 26 (1994), 61-63 · Zbl 0796.30014 · doi:10.1112/blms/26.1.61 |
[41] |
Koef W., Schmersau D., Weinstain’s functions and the Askey-Gasper indentity, URL: |
[42] |
Gradshtein I.S., Ryzhik I.M., Tablitsy integralov, summ, ryadov i proizvedenii, Fiziko-matematicheskaya literatura, M., 1951 |
[43] |
Aleksandrov I.A., Yuferova G.A., “Formula summirovaniya dlya polinomov Chebysheva i ee primenenie”, Vestnik TGU. Matematika i mekhanika, 2009, no. 2(6), 5-13 · Zbl 1515.33007 |
[44] |
Uitteker E.T., Vatson G.N., Kurs sovremennogo analiza, ch. 2, GTTN, M.; L., 1934 |
[45] |
Aleksandrov A.I., Aleksandrov I.A., “Tochnye otsenki proizvodnykh odnolistnykh funktsii”, Issledovaniya po matematicheskomu analizu i algebre, vyp. 3, TGU, Tomsk, 2001, 12-16 |
[46] |
Marty F., “Sur le module des coefficients de Maclaurin d”une function univalente”, Compt rend. Acad. Sci., 198 (1934), 1569-1571 · Zbl 0009.07602 |
[47] |
Littlewood J.E., Paley R.E., “A proof the an odd schlicht function has bounded coefficients”, J. London Math. Soc., s1-7:3 (1932), 167-169 · JFM 58.0367.01 · doi:10.1112/jlms/s1-7.3.167 |
[48] |
Robertson M.S., “A mark on the odd schlicht functions”, Bull. Amer. Math. Soc., 42:6 (1936), 366-370 · Zbl 0014.40702 · doi:10.1090/S0002-9904-1936-06300-7 |