×

Coefficient extremal problems for schlicht functions. (English) Zbl 0149.03605


Full Text: DOI

References:

[1] L. Bieberbach, Über die Koeffizienten derjenigen Potenzreihan, welche eine schlicht Abbildung des Einheitskreises vermittein, S.-B. Preuss. Akad. Wiss. Berlin (1916), 940-955. · JFM 46.0552.01
[2] Z. Charzyński and M. Schiffer, A new proof of the Bieberbach conjecture for the fourth coefficient., Arch. Rational Mech. Anal. 5 (1960), 187 – 193 (1960). · Zbl 0099.05901 · doi:10.1007/BF00252902
[3] Z. Charzyński and M. Schiffer, A geometric proof of the Bieberbach conjecture for the fourth coefficient, Scripta Math. 25 (1960), 173 – 181. · Zbl 0100.07301
[4] J. Clunie, On meromorphic schlicht functions, J. London Math. Soc. 34 (1959), 215 – 216. · Zbl 0087.07704 · doi:10.1112/jlms/s1-34.2.215
[5] P. R. Garabedian and M. Schiffer, A coefficient inequality for schlicht functions, Ann. of Math. (2) 61 (1955), 116 – 136. · Zbl 0065.30901 · doi:10.2307/1969623
[6] P. R. Garabedian and M. Schiffer, A proof of the Bieberbach conjecture for the fourth coefficient, J. Rational Mech. Anal. 4 (1955), 427 – 465. · Zbl 0065.06902
[7] G. M. Golusin, Geometrische Funktionentheorie, Hochschulbücher für Mathematik, Bd. 31, VEB Deutscher Verlag der Wissenschaften, Berlin, 1957 (German).
[8] Einar Hille, Analytic function theory. Vol. II, Introductions to Higher Mathematics, Ginn and Co., Boston, Mass.-New York-Toronto, Ont., 1962. · Zbl 0102.29401
[9] Eri Jabotinsky, Representation of functions by matrices. Application to Faber polynomials, Proc. Amer. Math. Soc. 4 (1953), 546 – 553. · Zbl 0052.30001
[10] Karl Löwner, Untersuchungen über schlichte konforme Abbildungen des Einheitskreises. I, Math. Ann. 89 (1923), no. 1-2, 103 – 121 (German). · JFM 49.0714.01 · doi:10.1007/BF01448091
[11] Z. Nehari and E. Netanyahu, On the coefficients of meromorphic schlicht functions, Proc. Amer. Math. Soc. 8 (1957), 15 – 23. · Zbl 0079.10004
[12] E. Netanyahu, Extremal problems for schlicht functions in the exterior of the unit circle, Canad. J. Math. 17 (1965), 335 – 341. · Zbl 0148.30804 · doi:10.4153/CJM-1965-033-3
[13] R. Nevanlinna, Über die konforme Abbildung von Sterngebieten, Finska Vetenskaps – Soc. Forhankl (A) 63 (1921-1922), No. 7. · JFM 48.0403.14
[14] H. Prawitz, Über Mittelwerte analytischer Funktionen, Ark. Mat. Astronom. Fys. 20 (1927-1928), 1-12. · JFM 53.0307.02
[15] W. C. Royster, Extremal problems for functions starlike in the exterior of the unit circle, Canad. J. Math. 14 (1962), 540 – 551. · Zbl 0104.29703 · doi:10.4153/CJM-1962-045-8
[16] W. C. Royster, Meromorphic starlike multivalent functions, Trans. Amer. Math. soc. 107 (1963), 300 – 308. · Zbl 0112.05101
[17] A. C. Schaeffer and D. C. Spencer, The coefficients of schlicht functions, Duke Math. J. 10 (1943), 611 – 635. · Zbl 0060.20404
[18] A. C. Schaeffer and D. C. Spencer, The coefficients of schlicht functions. II, Duke Math. J. 12 (1945), 107 – 125. · Zbl 0063.06763
[19] A. C. Schaeffer and D. C. Spencer, A variational method in conformal mapping, Duke Math. J. 14 (1947), 949 – 966. · Zbl 0029.25902
[20] A. C. Schaeffer and D. C. Spencer, Coefficient Regions for Schlicht Functions, American Mathematical Society Colloquium Publications, Vol. 35, American Mathematical Society, New York, N. Y., 1950. With a Chapter on the Region of the Derivative of a Schlicht Function by Arthur Grad. · Zbl 0049.06003
[21] A. C. Schaeffer, M. Schiffer, and D. C. Spencer, The coefficient regions of schlicht functions, Duke Math. J. 16 (1949), 493 – 527. · Zbl 0041.40903
[22] M. Schiffer, A method of variation within the family of simple functions, Proc. London Math. Soc. 44 (1938), 432-449. · Zbl 0019.22201
[23] -, On the coefficients of simple function, Proc. London Math. Soc. 44 (1938), 450-452. · Zbl 0019.22202
[24] Menahem Schiffer, Variation of the Green function and theory of the \?-valued functions, Amer. J. Math. 65 (1943), 341 – 360. · Zbl 0060.23705 · doi:10.2307/2371820
[25] -, Application of variational methods in the theory of conformal mappings, Proc. Sympos. Appl. Math. Vol. 8, pp. 93-113, Amer. Math. Soc., Providence, R. I., 1958.
[26] Menahem Schiffer, Extremum problems and variational methods in conformal mapping, Proc. Internat. Congress Math. 1958, Cambridge Univ. Press, New York, 1958, pp. 211 – 231.
[27] G. Springer, The coefficient problem for schlicht mappings of the exterior of the unit circle, Trans. Amer. Math. Soc. 70 (1951), 421 – 450. · Zbl 0042.31402
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.