| 从属解析函数族的有限阶哈达玛乘积 |
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| 引用本文： | 熊良鹏,刘晓丽.从属解析函数族的有限阶哈达玛乘积[J].数学物理学报(A辑),2014,34(1):150-156. |
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| 作者姓名： | 熊良鹏 刘晓丽 |
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| 作者单位： | 成都理工大学工程技术学院 四川 乐山 614007 |
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| 基金项目： | 成都理工大学工程技术学院科研发展基金(C122010003)资助. |
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| 摘 要： | 设PA,B]={f(z):f(z)(?)(1+Az)/(1-Bz),A+B≠0,|B|≤1,f(z)在单位开圆盘内解析}.定义函数族H_1,H_2,…,H_n的有限阶哈达玛乘积为H_1*H_2*H_3…*H_n(z)={f_1*f_2*f_3*…f_n(z):f_i∈H_i,i=1,2,…,n,n∈Z~+}.讨论并得到了P(A_1,B_1)*P(A_2,B_2)*P(A_3,B_3)*…*P(A_n,B_n)=P(X,Y)的充分必要条件,主要结果是对先前相应研究内容的直接推广.
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| 关 键 词： | 解析函数 从属 哈达玛乘积 充要条件. |
| 收稿时间： | 2012-06-07 |
| 修稿时间： | 2013-05-30 |
Hadamard Product of Finitely Order of Certain Class of Analytic Functions Defined by Subordination |
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| XIONG Liang-Peng,LIU Xiao-Li.Hadamard Product of Finitely Order of Certain Class of Analytic Functions Defined by Subordination[J].Acta Mathematica Scientia,2014,34(1):150-156. |
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| Authors: | XIONG Liang-Peng LIU Xiao-Li |
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| Institution: | School of Engineering Technology, Chengdu University of Technology, Sichuan Leshan 614007 |
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| Abstract: | Let P(A, B) denote a class of analytic functions subordinated to the function 1+Az/1-Bz, where A+B≠0, |B|≤1. The Hadamard product of finitely order of certain classes H 1, H2, …, Hn is defined by H1*H2*H3*…*Hn(z)={f1*f2*f3*… fn(z): fi ∈Hi, i =1, 2, …, n, n ∈Z+}. It obtains the necessary and sufficient conditions for equality P(A1, B1)*P(A2, B2)*P(A3, B3)*…*P(An, Bn)=P(X, Y), which extends the corresponding earlier results. |
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| Keywords: | Analytic functionzz Hadamard productzz Subordinationzz Necessary and sufficient conditionszz |
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