[1]吴东东,陈行堤.右半平面调和映照的卷积[J].华侨大学学报(自然科学版),2017,38(3):430-434.[doi:10.11830/ISSN.1000-5013.201703026]
　WU Dongdong,CHEN Xingdi.Convolution of Harmonic Mapping in Right-Half Plane[J].Journal of Huaqiao University(Natural Science),2017,38(3):430-434.[doi:10.11830/ISSN.1000-5013.201703026]
点击复制

右半平面调和映照的卷积()
分享到：

《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第38卷
期数:
2017年第3期
页码:
430-434
栏目:
出版日期:
2017-05-20

文章信息/Info

Title:
Convolution of Harmonic Mapping in Right-Half Plane
文章编号:
1000-5013(2017)03-0430-05
作者:
吴东东;  陈行堤
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
WU Dongdong;  CHEN Xingdi
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
调和映照;  卷积;  凸映照;  单叶性判别;  几何特征;  Cohn法则
Keywords:
harmonic mapping;  convolution;  convex mapping;  univalent criterion;  geometric properties;  Cohn’s rule
分类号:
O174.55
DOI:
10.11830/ISSN.1000-5013.201703026
文献标志码:
A
摘要:
研究右半平面调和映照卷积的单叶性判别和几何特征的刻画问题.证明第二复伸张为w(z)=-z×(z-a)/(1-az)(0≤a≤1)的右半平面调和映照f(z),其与典范右半平面调和映照f0(z)的卷积映照f*f0不仅属于S0H,而且是沿实轴方向上是凸的.
Abstract:
This paper is to give univalent criterions and to characterize the geometric properties for convolution of the right half-plane harmonic mapping f0(z)and f(z). If f0(z)is canonical and the second complex dilatation of f(z)is w(z)=-z(z-a)/(1-az), then the convolution function f*f0∈S0H and it is convex in the real axis provided 0≤a≤1.

参考文献/References:

[1] LEWY H.On the nonvanishing of the Jacobian in certain one-to-one mappings[J].Bulletin of the American Mathematical Society,1936,42(10):689-692.
[2] CLUNIE J G,SHEIL-SMALL T.Sheil-small, harmonic univalent functions[J].Annales Academi Scientiarum Fennic Series A I,1984,9(1):3-25.
[3] PONNUSAMY S,SINGH V.Convolution properties of some classes of analytic functions[J].Journal of Mathematical Sciences,1998,89(1):1008-1020.
[4] KUMAR R,DORFF M,GUPTA S,et al.Convolution properties of some harmonic mappings in the right half-plane[J].Bulletin of the Malaysian Mathematical Sciences Society,2016,39(1):439-455.
[5] DORFF M.Convolutions of planar harmonic convex mappings[J].Complex Variables Theory and Application An International Journal,2001,45(3):263-271.
[6] DORFF M,NOWAK M,WOLOSZKIEWICZ M.Convolutions of harmonic convex mappings[J].Complex Variables and Elliptic Equations,2012,57(5):489-503.
[7] LI Liulan,PONNUSAMY S.Solution to an open problem on convolutions of harmonic mappings[J].Complex Variables and Elliptic Equations,2013,58(12):1647-1653.
[8] JIANG Yueping,RASILA A,SUN Yong.A note on convexity of convolutions of harmonic mappings[J].Bulletin of the Korean Mathematical Society,2015,52(6):1925-1935.
[9] LI Liulan,PONNUSAMY S.Convolutions of slanted half-plane harmonic mappings[J].Analysis(Munich),2013,33(2):159-176.
[10] RAHMAN Q I,SCHMEISSER G.Analytic theory of polynomials, London mathematical society monographs new series[M].Oxford:Oxford University Press,2002:375-376.

相似文献/References:

[1]陈行堤.调和拟共形映照双曲雅可比的偏差性质[J].华侨大学学报(自然科学版),2010,31(3):351.[doi:10.11830/ISSN.1000-5013.2010.03.0351]
　CHEN Xing-di.Distortion Estimations of the Hyperbolic Jacobians of Harmonic Quasiconformal Mappings[J].Journal of Huaqiao University(Natural Science),2010,31(3):351.[doi:10.11830/ISSN.1000-5013.2010.03.0351]
[2]朱剑峰.单位圆上调和拟共形映照的复特征估计[J].华侨大学学报(自然科学版),2010,31(4):476.[doi:10.11830/ISSN.1000-5013.2010.04.0476]
　ZHU Jian-feng.Estimate for the Dilatation of Harmonic Quasiconformal Mappings in the Unit Disk[J].Journal of Huaqiao University(Natural Science),2010,31(3):476.[doi:10.11830/ISSN.1000-5013.2010.04.0476]
[3]朱剑峰,王朝祥,黄心中.单位圆上调和映照的单叶半径[J].华侨大学学报(自然科学版),2012,33(5):581.[doi:10.11830/ISSN.1000-5013.2012.05.0581]
　ZHU Jian-feng,WANG Chao-xiang,HUANG Xin-zhong.Univalent Radius of Harmonic Mapping in the Unit Disk[J].Journal of Huaqiao University(Natural Science),2012,33(3):581.[doi:10.11830/ISSN.1000-5013.2012.05.0581]
[4]李东征,陈行堤.调和映照的Landau定理[J].华侨大学学报(自然科学版),2012,33(5):584.[doi:10.11830/ISSN.1000-5013.2012.05.0584]
　LI Dong-zheng,CHEN Xing-di.Landau Theorem for Planar Harmonic Mappings[J].Journal of Huaqiao University(Natural Science),2012,33(3):584.[doi:10.11830/ISSN.1000-5013.2012.05.0584]
[5]占龙俊,黄心中.调和映照与像域为线性连结的剪切函数的关系[J].华侨大学学报(自然科学版),2015,36(5):603.[doi:10.11830/ISSN.1000-5013.2015.05.0603]
　ZHAN Long-jun,HUANG Xin-zhong.Relation Between Harmonic Mapping and Its Shear Function With Linearly Connected Image Domain[J].Journal of Huaqiao University(Natural Science),2015,36(3):603.[doi:10.11830/ISSN.1000-5013.2015.05.0603]
[6]王改华,李涛,吕朦,等.采用无监督学习算法与卷积的图像分类模型[J].华侨大学学报(自然科学版),2018,39(1):146.[doi:10.11830/ISSN.1000-5013.201703109]
　WANG Gaihua,LI Tao,Lü Meng,et al.Image Classification Model Using Unsupervised Learning Algorithm and Convolution[J].Journal of Huaqiao University(Natural Science),2018,39(3):146.[doi:10.11830/ISSN.1000-5013.201703109]
[7]李鸿萍.调和映照与调和K-拟共形映照的边界Schwarz引理[J].华侨大学学报(自然科学版),2022,43(2):279.[doi:10.11830/ISSN.1000-5013.202011023]
　LI Hongping.Boundary Schwarz Lemma for Harmonic Mappings and Harmonic K-Quasiconformal Mappings[J].Journal of Huaqiao University(Natural Science),2022,43(3):279.[doi:10.11830/ISSN.1000-5013.202011023]

备注/Memo

备注/Memo:
收稿日期: 2016-09-05
通信作者: 陈行堤(1976-),男,教授,博士,主要从事函数论的研究.E-mail:chxtt@hqu.edu.cn.
基金项目: 国家自然科学基金资助项目(11471128); 福建省自然科学基金资助项目(2014J01013); 华侨大学中青年教师科研提升计划项目(ZQN-YXl10); 华侨大学研究生科研创新能力培育计划项目(2016年度)
更新日期/Last Update: 2017-05-20