We studied the normality conditions in families of meromorphic functions, improved the results of Fang and Zalcman [Fang ML, Zalcman L, Normal families and shared values of meromorphic functions, Computational Methods...We studied the normality conditions in families of meromorphic functions, improved the results of Fang and Zalcman [Fang ML, Zalcman L, Normal families and shared values of meromorphic functions, Computational Methods and Function Theory, 2001, 1 （1）： 289-299], and generalized two new normality criterions. Let F be a family of meromorphic functions in a domain D, a a non-zero finite complex number, B a positive real number, and k and m two positive integers satisfying m〉2k＋4. If every function denoted by f belonging to F has only zeros with multiplicity at least k and satisfies f^m（z）f^（k）（Z）=α→ ｜^f（k）（z）｜ ≤B or f^m（z）f^（k）（z）=α→｜f（z）｜ ≥, then F is normal in D.展开更多
Recently,a class of Type Ⅱ factors has been constructed,arising from holomorphic coverings of bounded planar domains.Those operators in Type Ⅱ factors act on the Bergman space.In this paper,we develop new techniques...Recently,a class of Type Ⅱ factors has been constructed,arising from holomorphic coverings of bounded planar domains.Those operators in Type Ⅱ factors act on the Bergman space.In this paper,we develop new techniques to generalize those results to the case of the weighted Bergman spaces.In addition,a class of group-like von Neumann algebras are constructed,which are shown to be-isomorphic to the group von Neumann algebras.展开更多
文摘We studied the normality conditions in families of meromorphic functions, improved the results of Fang and Zalcman [Fang ML, Zalcman L, Normal families and shared values of meromorphic functions, Computational Methods and Function Theory, 2001, 1 （1）： 289-299], and generalized two new normality criterions. Let F be a family of meromorphic functions in a domain D, a a non-zero finite complex number, B a positive real number, and k and m two positive integers satisfying m〉2k＋4. If every function denoted by f belonging to F has only zeros with multiplicity at least k and satisfies f^m（z）f^（k）（Z）=α→ ｜^f（k）（z）｜ ≤B or f^m（z）f^（k）（z）=α→｜f（z）｜ ≥, then F is normal in D.
基金supported by National Natural Science Foundation of China (Grant No.11001078)Shanghai Municipal Education Commission and Shanghai Education Development Foundation (GrantNo. 11CG30)
文摘Recently,a class of Type Ⅱ factors has been constructed,arising from holomorphic coverings of bounded planar domains.Those operators in Type Ⅱ factors act on the Bergman space.In this paper,we develop new techniques to generalize those results to the case of the weighted Bergman spaces.In addition,a class of group-like von Neumann algebras are constructed,which are shown to be-isomorphic to the group von Neumann algebras.
