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Title:  Further results on factorization theory of meromorphic functions 
Authors:  Ng, TuenWai 
Issue Date:  1998 
Abstract:  In this thesis, we shall prove some results which, in turn, will allow us to solve some factorization problems in a systematic way. Also, we shall utilize new methods from theory of complex analytic sets and local holomorphic dynamlics to solve some factorization problems.
In Chapter 3, by using an extended version of Steinmetz's theorem, we prove that certain class of meromorphic functions is pseudoprime. Hence, we can prove that under certain conditions, R(z)H(z) is pseudoprime, where R(z) is a nonconstant rational function and H(z) is a finite order periodic function. In Chapter 4, we try to find out all possible factorizations of p(z)H(z) when H is an exponential type periodic function and p is a nonconstant polynomial. This confirms a conjecture of G.D. Song and C.C. Yang.
In Chapter 5, we shall use results from theory of complex analytic sets to prove certain criteria on the existence of a nonlinear entire common right factor of two entire functions. Applying these criteria, we can then prove that if f is an entire function which is pseudoprime and not of the form H(Q(z)), where H is a periodic entire function and Q is a polynomial, then R(f(z)) is also pseudoprime for any nonconstant rational function R. This result essentially solves a problem of G.D. Song and is a fundamental property of pseudoprime function. We also give other applications of these criteria to unique factorization problems. In Chapter 6, we consider the unique factorization problems of f o p and p o f where f is a prime transcendental entire function and p is prime polynomal. We shall use methods from local holomorphic dynamics to solve these problems. 
Description:  Thesis (Ph.D.)Hong Kong University of Science and Technology, 1998 ix, 99 leaves ; 30 cm HKUST Call Number: Thesis MATH 1998 Ng 
URI:  http://hdl.handle.net/1783.1/1658 
Appears in Collections:  MATH Doctoral Theses

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