| Normal Families and Uniqueness of Entire Functions and Their Derivatives |
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| 引用本文： | Jiang Ming CHANG Ming Liang FANG. Normal Families and Uniqueness of Entire Functions and Their Derivatives[J]. 数学学报(英文版), 2007, 23(6): 973-982. DOI: 10.1007/s10114-005-0861-5 |
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| 作者姓名： | Jiang Ming CHANG Ming Liang FANG |
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| 作者单位： | [1]Department of Mathematics, Changshu Institute of Technology, Changshu 215500, P. R. China [2]Department of Mathematics, Nanjing Normal University, Nanjing 210097, P. R. China [3]Department of Applied Mathematics, South China Agricultural University, Guangzhou 510642, P. R. China [4]Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100800, P. R. China |
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| 基金项目： | Supported by the NNSF of China （Grant No. 10471065）, the NSF of Education Department ot Jiangsu Provnce （Grant No. 04KJD110001）, the SRF for R0CS, SEM., and the Presidential Foundation of South China Agri- cultural University |
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| 摘 要： | Let f be a nonconstant entire function; let k ≥ 2 be a positive integer; and let a be a nonzero complex number. If f（z） = a→f′（z） = a, and f′（z） = a →f^（k）（z） = a, then either f = Ce^λz ＋ a or f = Ce^λz ＋ a（λ - 1）/）λ, where C and ）, are nonzero constants with λ^k-1 = 1. The proof is based on the Wiman-Vlairon theory and the theory of normal families in an essential way.
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| 关 键 词： | 完整函数 常态族 唯一性理论 正整数 |
| 收稿时间： | 2004-03-30 |
| 修稿时间： | 2004-03-302005-04-26 |
Normal Families and Uniqueness of Entire Functions and Their Derivatives |
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| Jiang Ming Chang,Ming Liang Fang. Normal Families and Uniqueness of Entire Functions and Their Derivatives[J]. Acta Mathematica Sinica(English Series), 2007, 23(6): 973-982. DOI: 10.1007/s10114-005-0861-5 |
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| Authors: | Jiang Ming Chang Ming Liang Fang |
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| Affiliation: | (1) Department of Mathematics, Changshu Institute of Technology, Changshu 215500, P. R. China;(2) Department of Mathematics, Nanjing Normal University, Nanjing 210097, P. R. China;(3) Department of Applied Mathematics, South China Agricultural University, Guangzhou 510642, P. R. China;(4) Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100800, P. R. China |
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| Abstract: | Let f be a nonconstant entire function; let k ≥ 2 be a positive integer; and let a be a nonzero complex number. If f(z) = a ⇒. f'(z) = a, and f'(z) = a ⇒. f (k)(z) = a, then either f = Ce λz + a or f = Ce λz + a(λ - 1)/λ, where C and λ are nonzero constants with λ k-1 = 1. The proof is based on the Wiman–Valiron theory and the theory of normal families in an essential way. Supported by the NNSF of China (Grant No. 10471065), the NSF of Education Department of Jiangsu Province (Grant No. 04KJD110001), the SRF for ROCS, SEM., and the Presidential Foundation of South China Agricultural University |
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| Keywords: | entire function normal family unicity theorem |
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