THE EXTENSION OPERATOR IN BANACH SPACES FOR LOCALLY BIHOLOMORPHIC MAPPINGS  

作　　者：刘名生 朱玉灿 

机构地区：[1]Department of Mathematics, South China Normal University [2]Department of Mathematics, Fuzhou University

出　　处：《Acta Mathematica Scientia》2008年第3期711-720,共10页数学物理学报（B辑英文版）

基　　金：This research is partly supported by the National Natural Science Foundation of China (10471048); the Doctoral Foundation of the Education Committee of China(20050574002); the Natural Science Foundation of Fujian Province, China (Z0511013);the Education Commission Foundation of Fujian Province, China (JB04038)

摘　　要：In this article, the generalized Roper-Suffridge extension operator in Banach spaces for locally biholomorphic mappings is introduced. It is proved that this operator preserves the starlikeness on some domains in Banach spaces but does not preserves convexity for some cases. Moreover, the growth theorem, covering theorem, and the radius of starlikeness are discussed. Some results of Roper and Suffridge, Gong and Liu, Graham et al in C^n are extended to Hilbert spaces or Banach spaces.In this article, the generalized Roper-Suffridge extension operator in Banach spaces for locally biholomorphic mappings is introduced. It is proved that this operator preserves the starlikeness on some domains in Banach spaces but does not preserves convexity for some cases. Moreover, the growth theorem, covering theorem, and the radius of starlikeness are discussed. Some results of Roper and Suffridge, Gong and Liu, Graham et al in C^n are extended to Hilbert spaces or Banach spaces.

关 键 词：Biholomorphic starlike mapping biholomorphic convex mapping the Roper-Suffridge extension operator 

分 类 号：O177.2[理学—数学]