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Literatur
The regionD is not necessarily simply-connected, and soZ may be an isolated boundary point, entirely surrounded by points ofD.
F. Iversen, Recherches sur les fonctions inverses des fonctions méromorphes, Thèse, Helsingfors (1914), p. 13.
A. S. Besicovitch, Proc. London Math. Soc. (2)32 (1931), pp. 1–19.
W. Seidel, Trans. Amer. Math. Soc.36 (1934), pp. 201–226 (218).
See L. Bieberbach, Lehrbuch der Funktionentheorie2 (1927), p. 146.
M. L. Cartwright, Proc. Cambridge Phil. Soc.31 (1935) p. 26.
F. and M. Riesz, Verhandlungen des 4. skand. Math. Kongresses, Stockholm (1916).
See F. and M. Riesz, Verhandlungen des 4. skand. Math. Kongresses, Stockholm § 4.4.
R. Nevanlinna, Compt. Rend.199 (1934), pp. 512–515 and p. 548. [Added in the proofs] See also verhandlungen des 8. skand. Math. Kongresses Stockholm (1934), pp. 116–133. Theorem 1 on page 129 of the latter is false in the form stated. For an analytic function which is not a constant omits a set of values of positive harmonic measure near any pole or regular point. A single point is obviously a set of harmonic measure zero; and so we have a contradiction. The proof holds for the theorem as stated in Comptes Rendus; but I do not see how to modify it for a similar theorem IIc in § 5.2 of this paper holds if the setE is of harmonic measure zero with respect toevery region, but not if the set is of absolute harmonic measure zero in the sense of Nevanlinna.
See § 5.2. R. Nevanlinna, Compt. Rend.199 (1934), pp. 512–515
F. Iversen, Recherches sur les fonctions inverses des fonctions méromorphes, Thèse, Helaingfors, 1914, p. 27.
R. Nevanlinna, Commentarii Math. Helvetici2 (1930), pp. 236–252.
J. E. Littlewood, Journal of London Math. Soc.2 (1927), pp. 172–176.
See L. S. Bosanquet and M. L. Cartwright, Math. Zeitschr.37 (1933). p. 188–189. Theorem V.
W. Seidel, Trans. Amer. Math. Soc.34 (1932) p. 18, und36 (1934) p. 213.
N. Lusin and J. Privaloff, Ann. Scientifiques de l'Ecole Normale sup. (3)42 (1925) pp. 143–191.
See G. Julia, Leçons sur les fonctions uniformes (Paris 1923), Chap. I.
See L. Bieberbach. Lehrbuch der Funktionentheorie, II (1927), p. 266. The restriction α≦1/2 is only required to make 5/4αп<п, so that the contour used in this particular argument does not cross itself.
A. Plessner, Journ. f. Math.158 (1927), p. 219.
L. Ahlfors, Soc. Sci. Fen. Commentationes Phys. Math.5, 16 (1931), pp. 1–19.
—See § 2.1..
See G. Julia, Leçons sur les fonctions uniformes, Paris (1923) Chap. II.
A. Hurwitz.-R. Courant, Funktionentheorie, Berlin (1929) p. 432. See also J. E. Littlewood, Proc. London Math. Soc. (2)23 (1924), p.489.
A. S. Besicovitch, Proc. London Math. Soc. (2)32 (1931), pp. 1–19.
See W. Seidel, Trans. Amer. Math. Soc.36 (1934).
See § 4.4. W. Seidel, Trans. Amer. Math. Soc.36 (1934).
Compare R. Nevanlinna, Comptes Rendus199 (1934), pp. 512–515 and 548. See footnote R. Nevanlinna, Compt. Rend.199 (1934), pp. 512–515
W. Seidel, Trans. Amer. Math. Soc.36 (1934), p. 228.
See the theorem of R. Nevanlinna quoted in § 2. 1.
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Cartwright, M.L. On the behaviour of an analytic function in the neighbourhood of its essential singularities. Math. Ann. 112, 161–186 (1936). https://doi.org/10.1007/BF01565413
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DOI: https://doi.org/10.1007/BF01565413