两类双全纯映照子族在Roper-Suffridge延拓算子下的不变性  

The Invariance of Two Subclasses of Biholomorphic Mappings Under the Roper-Suffridge Extension Operators

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作  者:王朝君 崔艳艳 刘浩[2] Chaojun Wang;Yanyan Cui;Hao Liu(College of Mathematics and Statistics, Zhoukou Normal University, Henan Zhoukou 466001;Institute of Contemporary Mathematics, Henan University, Henan Kaifeng 475001)

机构地区:[1]周口师范学院数学与统计学院,河南周口466001 [2]河南大学现代数学研究所,河南开封475001

出  处:《数学物理学报(A辑)》2019年第2期209-219,共11页Acta Mathematica Scientia

基  金:国家自然科学基金(11271359;11471098);河南省教育厅科学技术研究重点项目(17A110041;19B110016);周口师范学院科研创新基金项目(ZKNUA201805)~~

摘  要:该文将已有的Roper-Suffridge延拓算子在Bergman-Hartogs域上进行了推广,应用α次β型螺形映照及复数λ阶殆星映照的几何性质及增长定理,讨论了推广后的RoperSuffridge延拓算子在Bergman-Hartogs域上保持α次β型螺形性及复数λ阶殆星性,并得到一些特殊情况.所得结论为构造多复空间中的α次β型螺形映照及复数λ阶殆星映照提供了新的途径.In this paper, we generalize the Roper-Suffridge operator on Bergman-Hartogs domains. Applying the geometric properties and the growth theorems of spirallike mappings of type β and order α as well as almost starlike mappings of complex order λ, we obtain that the generalized Roper-Suffridge operators preserve spirallikeness of type β and order α as well as almost starlikeness of complex order λ on Bergman-Hartogs domains which lead to some special cases. The conclusions provide new approaches to construct spirallike mappings of type β and order α and almost starlike mappings of complex order λ in several complex variables.

关 键 词:ROPER-SUFFRIDGE算子 双全纯映照 Bergman-Hartogs域 

分 类 号:O174.56[理学—数学]

 

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