On the multivalency of analytic functions

Toshio UMEZAWA

doi:10.2969/jmsj/00430279

Toshio UMEZAWA

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ジャーナルフリー

1952 年 4 巻 3-4 号 p. 279-285

DOI https://doi.org/10.2969/jmsj/00430279

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Published: 1952 Received: 1952/01/10 Available on J-STAGE: 2006/08/29 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/08/29 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Right : [1] K. Noshiro, On the univalency of certain analytic functions, Journ. Fac. Sci. Hokkaido Imp. Univ. (1) 2, Nos. 1-2 (1934), pp. 89-101.
[2] J. Dieudonné, Recherches sur quelques problèmes relatifs aux polynomes et aux fonctions bornées d'une variable complexe, Thèse de Paris, Ann. Sci. Ecole Norm. Sup. Vol. 48 (1931), pp. 248-358.
[3] E. Sakai, On the multivalency of analytic functions, J. Math. Soc. Japan. vol. 2, Nos. 1-2 (1950), pp 105-113.
[4] Z. Nehari, The radius of univalence of analytic functions, Amer. J. Math. vol. LXXI, No. 4 (1949).
[5] We mean by ψ (z)⊂T that the set of values taken by ψ (z) in D belongs to the domain T.
[6] The positive quantity Ω (α, T) depends only on α and T, and neither on the selection of the mapping function nor on that of the branch g(t) of the mapping function. See [1], foot-notes at p. 90.
[7] G. Szegö, Über orthogonale Polynome, die zu einer gegebenen Kurve der komplexen Ebene gehören, Math. Zeit. vol. 9 (1921), pp. 218-270.
[8] P. R. Garabedian, Schwarz's lemma and the Szegö kernel function, Trans. Amer. Math. Soc. Vol. 67 (1949), pp. 1-35.
[9] L. V. Ahlfors, Bounded analytic functions, Duke Math. J. vol. 14 (1947), pp. 1-14.
[10] P. R. Garabedian, loc. cit.
[11] S. Ozaki, Some remarks on the univalency and multivalency of functions, Sci. Rep. of Tokyo Bunrika Daigaku Nos. 31-32 (1934), p. 49.
[12] A. W. Goodman, On the Schwarz-Christoffel transformation and p-valent functions, Trans. Amer. Math. Soc. vol. 68 (1950), p. 211.
[13] S. Ozaki, On the theory of multivalent functions II, Sci. Rep. T.B.D. vol. 4, No. 77 (1941), p. 57.
[14] K. Noshiro, On the theory of schlicht functions, Journ. Fac. Sci. Hokkaido Imp. Univ. (1) vol. 2, No. 3 (1934), pp. 129-155.
[15] T. Umezawa, Analytic functions convex in one direction, J. Math. Soc. Japan Vol. 4, No. 2 (1952), pp. 194-202.

訂正日: 2006/08/29 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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