Normal families of holomorphic functions and multiple values
نویسندگان
چکیده
منابع مشابه
Composite Holomorphic Functions and Normal Families
and Applied Analysis 3 Remark 1.5. In Theorem 1.2 setting α z constant zero and P z,w a polynomial in variable w that vanishes exactly on a finite set of holomorphic functions S, we obtain Corollary 1.6 which generalizes the famous Montel’s criterion that a holomorphic family omitting 2 or more values is normal. Corollary 1.6. Let F be a family of holomorphic functions on a domain D. Let S be a...
متن کاملNormal Families of Bicomplex Holomorphic Functions
In this article, we introduce the concept of normal families of bicomplex holomorphic functions to obtain a bicomplex Montel theorem. Moreover, we give a general definition of Fatou and Julia sets for bicomplex polynomials and we obtain a characterization of bicomplex Fatou and Julia sets in terms of Fatou set, Julia set and filled-in Julia set of one complex variable. Some 3D visual examples o...
متن کاملExceptional values in holomorphic families of entire functions
For a holomorphic family of entire functions we study dependence of Picard exceptional values of these functions on the parameter. In 1926, Julia [5] studied singularities of implicit functions defined by equations f(z, w) = 0, where f is an entire function of two variables such that f(., w) 6≡ 0 for every w ∈ C. Among other things, he investigated the exceptional set P consisting of those w fo...
متن کامل2 Quantum Normal Families : Normal Families of Holomorphic Functions and Mappings on a Banach Space
The authors lay the foundations for the study of normal families of holomorphic functions and mappings on an infinitedimensional normed linear space. Characterizations of normal families, in terms of value distribution, spherical derivatives, and other geometric properties are derived. Montel-type theorems are established. A number of different topologies on spaces of holomorphic mappings are c...
متن کاملNormal families of meromorphic functions sharing values or functions
* Correspondence: jiangyunbo@ss. buaa.edu.cn School of Mathematics and Systems Science and LMIB, Beihang University, Beijing, 100191, People’s Republic of China Abstract In this paper, we investigate the normal families of meromorphic functions concerning shared values and shared analytic functions and prove some normal criteria that generalize or extend some results obtained by Q. C. Zhang, Y....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the Belgian Mathematical Society - Simon Stevin
سال: 2012
ISSN: 1370-1444
DOI: 10.36045/bbms/1347642381