Further Results On Factorization Theory Of Meromorphic Functions

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Further Results On Factorization Theory Of Meromorphic Functions

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Author :
language : en
Publisher:
Release Date :

Further Results On Factorization Theory Of Meromorphic Functions written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

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 pseudo-prime. Hence, we can prove that under certain conditions, R(z)H(z) is pseudo-prime, where R(z) is a non-constant 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 non-constant 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 non-linear entire common right factor of two entire functions. Applying these criteria, we can then prove that if f is an entire function which is pseudo-prime 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 pseudo-prime for any non-constant rational function R. This result essentially solves a problem of G.D. Song and is a fundamental property of pseudo-prime 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.

Fix Points And Factorization Of Meromorphic Functions Topics In Complex Analysis

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Author : Chung-chun Yang
language : en
Publisher: World Scientific
Release Date : 1990-01-01

Fix Points And Factorization Of Meromorphic Functions Topics In Complex Analysis written by Chung-chun Yang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-01 with Mathematics categories.

The fix-points and factorization of meromorphic functions have become two research topics that have attracted many complex analysts' attention throughout the world; notably in U.S., China, and Japan. The first two chapters reintroduce Nevanlinna's theory of meromorphic functions and Montel's normal families theory for entire functions. Based on these, several theorems on fix-points were derived. The last two chapters introduce the factorization theory and the relationships between the fix-points and factorization; many recent results in factorization theory were reported and related open questions were raised for further study. This book provides a timely introduction to some of the topics that are currently pursued by many complex analysts. For instance, the fix-points of itrates of functions is closely related to the fractal mathematics, which has just been realized to be useful in many branches of engineering and physics as well as in computer graphics.

Fix Points And Factorization Of Meromorphic Functions

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Author : Qitai Zhuang
language : en
Publisher: World Scientific
Release Date : 1990

Fix Points And Factorization Of Meromorphic Functions written by Qitai Zhuang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.

The fix-points and factorization of meromorphic functions have become two research topics that have attracted many complex analysts' attention throughout the world; notably in U.S., China, and Japan. The first two chapters reintroduce Nevanlinna's theory of meromorphic functions and Montel's normal families theory for entire functions. Based on these, several theorems on fix-points were derived. The last two chapters introduce the factorization theory and the relationships between the fix-points and factorization; many recent results in factorization theory were reported and related open questions were raised for further study. This book provides a timely introduction to some of the topics that are currently pursued by many complex analysts. For instance, the fix-points of itrates of functions is closely related to the fractal mathematics, which has just been realized to be useful in many branches of engineering and physics as well as in computer graphics.

Factorization Theory Of Meromorphic Functions And Related Topics

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Author : Chung-Chun Yang
language : en
Publisher:
Release Date : 1982

Factorization Theory Of Meromorphic Functions And Related Topics written by Chung-Chun Yang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Mathematics categories.

Complex Analysis Kentucky 1976

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Author : J. D. Buckholtz
language : en
Publisher: Springer
Release Date : 2006-11-14

Complex Analysis Kentucky 1976 written by J. D. Buckholtz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

Meromorphic Functions Over Non Archimedean Fields

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Author : Pei-Chu Hu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Meromorphic Functions Over Non Archimedean Fields written by Pei-Chu Hu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Nevanlinna theory (or value distribution theory) in complex analysis is so beautiful that one would naturally be interested in determining how such a theory would look in the non Archimedean analysis and Diophantine approximations. There are two "main theorems" and defect relations that occupy a central place in N evanlinna theory. They generate a lot of applications in studying uniqueness of meromorphic functions, global solutions of differential equations, dynamics, and so on. In this book, we will introduce non-Archimedean analogues of Nevanlinna theory and its applications. In value distribution theory, the main problem is that given a holomorphic curve f : C -+ M into a projective variety M of dimension n and a family 01 of hypersurfaces on M, under a proper condition of non-degeneracy on f, find the defect relation. If 01 n is a family of hyperplanes on M = r in general position and if the smallest dimension of linear subspaces containing the image f(C) is k, Cartan conjectured that the bound of defect relation is 2n - k + 1. Generally, if 01 is a family of admissible or normal crossings hypersurfaces, there are respectively Shiffman's conjecture and Griffiths-Lang's conjecture. Here we list the process of this problem: A. Complex analysis: (i) Constant targets: R. Nevanlinna[98] for n = k = 1; H. Cartan [20] for n = k > 1; E. I. Nochka [99], [100],[101] for n > k ~ 1; Shiffman's conjecture partially solved by Hu-Yang [71J; Griffiths-Lang's conjecture (open).

Factorization Of Meromophic Functions

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Author : United States. Naval Research Office
language : en
Publisher:
Release Date : 1972

Factorization Of Meromophic Functions written by United States. Naval Research Office and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Factors (Algebra) categories.

On Periodic Left Factors Of Meromorphic Functions

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Author : Fred Gross
language : en
Publisher:
Release Date : 1969

On Periodic Left Factors Of Meromorphic Functions written by Fred Gross and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Functions, Meromorphic categories.

Review

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Author :
language : en
Publisher:
Release Date : 1982

Review written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Naval research categories.

Entire Functions And Related Parts Of Analysis

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Author : Jacob Korevaar
language : en
Publisher: American Mathematical Soc.
Release Date : 1968-12-31

Entire Functions And Related Parts Of Analysis written by Jacob Korevaar and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968-12-31 with Mathematics categories.