Book Review
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MathSciNet review:
1568168
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Book Information:
Author:
Chi-tai Chuang
Title:
Normal families of meromorphic functions
Additional book information:
World Scientific, Singapore, 1993, xi+473 pp., US$68.00. ISBN 981-02-1257-7.
Author:
Joel L. Schiff
Title:
Normal families
Additional book information:
Springer, New York, 1993, ix+236 pp., US$39.00. ISBN 0-387-97967-0.
Daniel S. Alexander, A history of complex dynamics, Aspects of Mathematics, E24, Friedr. Vieweg & Sohn, Braunschweig, 1994. From Schröder to Fatou and Julia. MR 1260930, DOI 10.1007/978-3-663-09197-4
Walter Bergweiler and Alexandre Eremenko, On the singularities of the inverse to a meromorphic function of finite order, Rev. Mat. Iberoamericana 11 (1995), no. 2, 355–373. MR 1344897, DOI 10.4171/RMI/176
W. Bergweiler and W. H. J. Fuchs, On the zeros of the second derivative of real entire functions, J. Anal. 1 (1993), 73–79. MR 1230507
[4] A. Bloch, La conception actuelle de la théorie des fonctions entirés et méromorphes, Enseign. Math. 25 (1926), 83-103.
Yong Xing Ku, A criterion for normality of families of meromorphic functions, Sci. Sinica Special Issue I on Math. (1979), 267–274 (Chinese, with French summary). MR 662205
W. K. Hayman, Research problems in function theory, The Athlone Press [University of London], London, 1967. MR 0217268
Einar Hille, Analytic function theory. Vol. II, Introductions to Higher Mathematics, Ginn and Company, Boston, Mass.-New York-Toronto, Ont., 1962. MR 0201608
Serge Lang, Introduction to complex hyperbolic spaces, Springer-Verlag, New York, 1987. MR 886677, DOI 10.1007/978-1-4757-1945-1
[9] P. Montel, Leçons sur les familles normales de fonctions analytiques et leurs applications, Gauthier-Villars, Paris, 1927.
I. B. Oshkin, On a condition for the normality of families of holomorphic functions, Uspekhi Mat. Nauk 37 (1982), no. 2(224), 221–222 (Russian). MR 650781
Xue Cheng Pang, Bloch’s principle and normal criterion, Sci. China Ser. A 32 (1989), no. 7, 782–791. MR 1057999
Xue Cheng Pang, On normal criterion of meromorphic functions, Sci. China Ser. A 33 (1990), no. 5, 521–527. MR 1070538
Wilhelm Schwick, Normality criteria for families of meromorphic functions, J. Analyse Math. 52 (1989), 241–289. MR 981504, DOI 10.1007/BF02820480
Wilhelm Schwick, Repelling periodic points in the Julia set, Bull. London Math. Soc. 29 (1997), no. 3, 314–316. MR 1435565, DOI 10.1112/S0024609396007035
Lawrence Zalcman, A heuristic principle in complex function theory, Amer. Math. Monthly 82 (1975), no. 8, 813–817. MR 379852, DOI 10.2307/2319796
[16] -, Normal families revisited, Complex Analysis and Related Topics (J. J. O. O. Wiegerinck, ed.), Univ. of Amsterdam, Amsterdam, 1993, pp. 149-164.
- [1]
- Daniel S. Alexander, A history of complex dynamics: From Schroder to Fatou and Julia, Vierweg, Braunschweig, 1994. MR 1260930 (95d:01014)
- [2]
- Walter Bergweiler and Alexandre Eremenko, On the singularities of the inverse to a meromorphic function of finite order, Rev. Mat. Iberoamericana (to appear). MR 1344897 (96h:30055)
- [3]
- W. Bergweiler and W. H. J. Fuchs, On the zeros of the second derivative of real entire functions, J. Anal. 1 (1993), 73-79. MR 1230507 (94m:30051)
- [4]
- A. Bloch, La conception actuelle de la théorie des fonctions entirés et méromorphes, Enseign. Math. 25 (1926), 83-103.
- [5]
- Y. Gu [Ku], A criterion for normality of families of meromorphic functions, Sci. Sinica 1 (special issue) (1979), 267-274. (Chinese) MR 662205 (83i:30047)
- [6]
- W. K. Hayman, Research problems in function theory, Athlone Press, London, 1964. MR 0217268 (36:359)
- [7]
- E. Hille, Analytic function theory, Vol. 2, Ginn, Boston, 1962. MR 0201608 (34:1490)
- [8]
- S. Lang, Introduction to complex hyperbolic spaces, Springer, New York, 1987. MR 886677 (88f:32065)
- [9]
- P. Montel, Leçons sur les familles normales de fonctions analytiques et leurs applications, Gauthier-Villars, Paris, 1927.
- [10]
- I. B. Oshkin, On a test of normality of families of analytic families, Math. Surveys 37 (1982), 237-238. MR 650781 (83f:30026)
- [11]
- Xue-Cheng Pang, Bloch's principle and normal criterion, Sci. China Ser. A 32 (1989), 782-791. MR 1057999 (91i:30031)
- [12]
- -, On normal criterion of meromorphic functions, Sci. China Ser. A 33 (1990), 521-527. MR 1070538 (92b:30041)
- [13]
- W. Schwick, Normality criteria for families of meromorphic functions, J. Anal. Math. 52 (1989), 241-289. MR 981504 (90k:30061)
- [14]
- -, Repelling periodic points in the Julia set, Bull. London. Math. Soc. (to appear). MR 1435565 (97m:30029)
- [15]
- L. Zalcman, A heuristic principle in complex function theory, Amer. Math. Monthly 82 (1975), 813-817. MR 0379852 (52:757)
- [16]
- -, Normal families revisited, Complex Analysis and Related Topics (J. J. O. O. Wiegerinck, ed.), Univ. of Amsterdam, Amsterdam, 1993, pp. 149-164.
Review Information:
Reviewer:
David Drasin
Journal:
Bull. Amer. Math. Soc.
32 (1995), 257-261
DOI:
https://doi.org/10.1090/S0273-0979-1995-00573-2
