调和线性微分算子的半径问题  

The Problem of the Radii of a Harmonic Linear Differential Operator

作　　者：扈振永 王麒翰 龙波涌[1] Hu Zhenyong;Wang Qihan;Long Boyong(School of Mathematic Sciences,Anhui University,Hefei 230601)

机构地区：[1]安徽大学数学科学学院,合肥230601

出　　处：《数学物理学报（A辑）》2020年第5期1163-1174,共12页Acta Mathematica Scientia

基　　金：国家自然科学基金(11501001);安徽省自然科学基金面上项目(1908085MA18);安徽大学科研项目(Y01002428)。

摘　　要：对于单位圆盘上的调和映射fi(z)=hi(z)+gi(z)(i=1,2)的系数满足给定的条件,研究凸组合(1−t)Lϵf1+tLϵf2的α阶完全凸半径及α阶完全星形半径,其中Lϵfi=zfiz−ϵzfiz(|ϵ|=1)表示fi的微分算子.此外,给出调和映射的卷积在微分算子下的α阶完全凸半径及α阶完全星形半径.所得结果均为最佳.For harmonic mappings fi(z)=hi(z)+gi(z)(i=1,2)defined in the unit disk satisfying the given coefficient conditions,we consider the radii of full convexity and full starlikeness of orderαfor the convex combination(1−t)Lϵf1+tLϵf2,where Lϵfi=z∂fi∂z−ϵz-fi∂z(|ϵ|=1)denotes the differential operator of fi.In addition,we obtain the radii of fully convex and full starlikeness of orderαfor convolution of harmonic mappings under the differential operator.All results are sharp.

关 键 词：调和映射 凸组合 α阶完全凸 α阶完全星形 

分 类 号：O174.5[理学—数学]