Please use this identifier to cite or link to this item:
https://ah.lib.nccu.edu.tw/handle/140.119/52850
題名: | A 類半純函數之某些值分佈 Some value distribution of Meromorphic functions of Class A |
作者: | 陳盈穎 Chen, Ying Ying |
貢獻者: | 陳天進 Chen, Ten Ging 陳盈穎 Chen, Ying Ying |
關鍵詞: | 值分佈理論 半純函數 A類半純函數 Value Distribution Theory Meromorphic Function Meromorphic Function of Class A |
日期: | 2011 | 上傳時間: | 17-四月-2012 | 摘要: | 在這篇論文裡,我們探討 $\\mathcal{A}$ 類半純函數的值分佈基本理論。我們證明了每一個 $\\mathcal{A}$ 類半純函數最多有兩個重值,而這個結果是最佳的情形。進而,我們證明若一個 $\\mathcal{A}$ 類半純函數 $f$ 與其導數 $f^{(k)}$ 共非零的複數值,則 $f\\equiv f^{(k)}$。 In this thesis, we study the basic theory of value distribution of meromorphic function of class $\\mathcal{A}$. We prove that every meromorphic function of class $\\mathcal{A}$ has at most two multiple values and the result is sharp. Also, we prove that if a meromorphic function $f$ of class $\\mathcal{A}$ and its derivative $f^{(k)}$ share a non-zero complex value, then $f\\equiv f^{(k)}$. |
參考文獻: | [1] C.-T. Chuang and C.-C. Yang, Fix-points and factorization of meromorphic functions, World Scienti c Publishing Co. Inc., Teaneck, NJ, 1990. Translated from the Chinese. [2] G. Frank and G. Wei enborn, Meromorphe Funktionen, die mit einer ihrer Ableitungen Werte teilen, Complex Variables Theory Appl., 7 (1986), pp. 33{43. [3] F. Gross, Factorization of meromorphic functions, Mathematics Research Center, Naval Research Laboratory, Washington, D. C., 1972. [4] G. G. Gundersen, Meromorphic functions that share three or four values, J. London Math. Soc. (2), 20 (1979), pp. 457{466. [5] , Meromorphic functions that share four values, Trans. Amer. Math. Soc., 277 (1983), pp. 545{567. [6] W. K. Hayman, Meromorphic functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964. [7] H. Milloux, Les fonctions m eromorphes et leurs d eriv ees. Extensions d`un th eor eme de M. R. Nevanlinna. Applications, Actualit es Sci. Ind., no. 888, Hermann et Cie., Paris, 1940. [8] R. Nevanlinna, Le th eor eme de Picard-Borel et la th eorie des fonctions m eromorphes, Chelsea Publishing Co., New York, 1974. Reprinting of the 1929 original. [9] C.-C. Yang and H.-X. Yi, Uniqueness theory of meromorphic functions, vol. 557 of Mathematics and its Applications, Kluwer Academic Publishers Group, Dordrecht, 2003. [10] L. Yang, Value distribution theory, Springer-Verlag, Berlin, 1993. Translated and revised from the 1982 Chinese original. |
描述: | 碩士 國立政治大學 應用數學研究所 98751003 100 |
資料來源: | http://thesis.lib.nccu.edu.tw/record/#G0987510031 | 資料類型: | thesis |
Appears in Collections: | 學位論文 |
Files in This Item:
File | Size | Format | |
---|---|---|---|
003101.pdf | 688.37 kB | Adobe PDF2 | View/Open |
Google ScholarTM
Check
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.