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| Title: | 探討半純函數指定兩個值之相關問題
On meromorphic functions with two prescribed values |
| Authors: | 張靜華
Chang, Ching Hua |
| Contributors: | 陳天進
Chen, Ten Ging
張靜華
Chang, Ching Hua |
| Keywords: | 半純函數
Prescribed Values |
| Date: | 2009 |
| Issue Date: | 2016-05-09 15:25:42 (UTC+8) |
| Abstract: | 在這篇論文裡，我們探討半純函數指定兩個值之相關問題。特別地，我們探討純函數指定0-1集，同時，我們論證了有關離散型複數數列之一些有趣的結果，利用它們得到關於指定0-1集純函數存在性的必要條件。
In this thesis, we study meromorphic functions with two prescribed values. Especially, entire functions with prescribed zero-one sets. Also, we develop the growth criterion for discrete complex sequences and obtain some interesting results. Using the order of discrete sequences, we obtain a necessary condition for the existence of entire functions with prescribed zero-one set.
謝辭 i
Abstract ii
中文摘要 iii
Introduction 1
Meromorphic Functions with Prescribed Zero-Pole Sets 2
The Growth of Discrete Sequences 6
Basic Theory of Value Distribution 18
Entire Functions with Prescribed Zero-One Sets 25
References 34 |
| Reference: | [1] L. V. Ahlfors, Complex analysis, Third edition,McGraw-Hill, 1979.
[2] J. B. Conway, Functions of one complex variable, Second
edition, Springer-Verlag, 1973.
[3] F. Gross, Factorization of meromorphic functions, U. S.
Government Printing Office, Washington, D. C. , 1972.
[4] W. K. Hayman, Meromorphic functions, Clarendon Press,
Oxford, 1964.
[5] R. Nevanlinna, Le theoreme de Picard-Borel et la theorie des fonctions meromorphes, Gauthiers-Villars,
Paris, 1929.
[6] M. Ozawa, On the zero-one set of an entire function, Kodai Math. J. , 2 (1979), 194--199.
[7] L. A. Rubel and C. C. Yang, Interpolation and unavoidable families of meromorphic functions, Mich. Math. J. , 20 (1973), 289--296.
[8] L. Yang, Value distribution theory, Berlin Heidelberg:
Springer-Verlag, Beijing:Science Press, 1993.
[9] C. C. Yang and C. T. Chuang, Fixed points and factorization theory of meromorphic functions, Peking Univ. Press, 1988.
[10] C. C. Yang and H. X. Yi, Uniqueness Theory of Meromorphic Functions, Kluwer Academic Publishers, 2003.
[11] H. X. Yi, Some theorems on systems of meromorphic
functions, J. Shandong Univ. , 32 (1997), No.3, 241--247. |
| Description: | 碩士
國立政治大學
應用數學系
96972001 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0096972001 |
| Data Type: | thesis |
| Appears in Collections: | [應用數學系] 學位論文
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