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On The Value Distribution Of Meromorphic Functions With Their Derivatives

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On The Value Distribution Of Meromorphic Functions With Their Derivatives

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Author :
language : en
Publisher:
Release Date : 2008

On The Value Distribution Of Meromorphic Functions With Their Derivatives written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.

Value Distribution Of Meromorphic Functions And Their Derivatives

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Author : Daniel A. Nicks
language : en
Publisher:
Release Date : 2010

Value Distribution Of Meromorphic Functions And Their Derivatives written by Daniel A. Nicks and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.

The content of this thesis can be divided into two broad topics. The first half investigates the deficient values and deficient functions of certain classes of meromorphic functions. Here a value is called deficient if a function takes that value less often than it takes most other values. It is shown that the derivative of a periodic meromorphic function has no finite non-zero deficient values, provided that the function satisfies a necessary growth condition. The classes B and S consist of those meromorphic functions for which the finite critical and asymptotic values form a bounded or finite set. A number of results are obtained about the conditions under which members of the classes B and S and their derivatives may admit rational, or slowly-growing transcendental, deficient functions. The second major topic is a study of real functions -- those functions which are real on the real axis. Some generalisations are given of a theorem due to Hinkkanen and Rossi that characterizes a class of real meromorphic functions having only real zeroes, poles and critical points. In particular, the assumption that the zeroes are real is discarded, although this condition reappears as a conclusion in one result. Real entire functions are the subject of the final chapter, which builds upon the recent resolution of a long-standing conjecture attributed to Wiman. In this direction, several conditions are established under which a real entire function must belong to the classical Laguerre-Polya class LP. These conditions typically involve the non-real zeroes of the function and its derivatives.

Value Distribution Of Meromorphic Functions

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Author : Jianhua Zheng
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-31

Value Distribution Of Meromorphic Functions written by Jianhua Zheng 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 2011-03-31 with Mathematics categories.

"Value Distribution of Meromorphic Functions" focuses on functions meromorphic in an angle or on the complex plane, T directions, deficient values, singular values, potential theory in value distribution and the proof of the celebrated Nevanlinna conjecture. The book introduces various characteristics of meromorphic functions and their connections, several aspects of new singular directions, new results on estimates of the number of deficient values, new results on singular values and behaviours of subharmonic functions which are the foundation for further discussion on the proof of the Nevanlinna conjecture. The independent significance of normality of subharmonic function family is emphasized. This book is designed for scientists, engineers and post graduated students engaged in Complex Analysis and Meromorphic Functions. Dr. Jianhua Zheng is a Professor at the Department of Mathematical Sciences, Tsinghua University, China.

Value Distribution Of Meromorphic Functions

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Author : Anatoliĭ Asirovich Golʹdberg
language : en
Publisher: American Mathematical Soc.
Release Date :

Value Distribution Of Meromorphic Functions written by Anatoliĭ Asirovich Golʹdberg 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 with Mathematics categories.

"This book contains a comprehensive exposition of the Nevanlinna theory of meromorphic functions of one complex variable, with detailed study of deficiencies, value distribution, and asymptotic properties of meromorphic functions." "The main body of the book is a translation of the Russian original published in 1970, which has been one of the most popular sources in this field since then. New references and footnotes related to recent achievements in the topics considered in the original edition have been added and a few corrections made. A new Appendix with a survey of the results obtained after 1970 and extensive bibliography has been written by Alexandre Ermenko and James K. Langley for this English edition." "The only prerequisite for understanding material of this book is an undergraduate course in the theory of functions of one complex variable."--BOOK JACKET.

Value Distribution Theory

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Author : Yang Lo
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Value Distribution Theory written by Yang Lo 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 2013-04-17 with Mathematics categories.

It is well known that solving certain theoretical or practical problems often depends on exploring the behavior of the roots of an equation such as (1) J(z) = a, where J(z) is an entire or meromorphic function and a is a complex value. It is especially important to investigate the number n(r, J = a) of the roots of (1) and their distribution in a disk Izl ~ r, each root being counted with its multiplicity. It was the research on such topics that raised the curtain on the theory of value distribution of entire or meromorphic functions. In the last century, the famous mathematician E. Picard obtained the pathbreaking result: Any non-constant entire function J(z) must take every finite complex value infinitely many times, with at most one excep tion. Later, E. Borel, by introducing the concept of the order of an entire function, gave the above result a more precise formulation as follows. An entire function J (z) of order A( 0 A

Studies On Shared Values Of Meromorphic Functions

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Author : Jilong Zhang
language : en
Publisher:
Release Date : 2008

Studies On Shared Values Of Meromorphic Functions written by Jilong Zhang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Functions, Meromorphic categories.

This survey part of the thesis contains some background to the series of studies on shared values of meromorphic functions. Nevanlinna's value distribution theory and some classical results are introduced. Meromorphic functions sharing values with their derivatives and two differential polynomials sharing one small function are studied. A short summary of the articles is included.

Complex Analysis I

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Author : A.A. Gonchar
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11

Complex Analysis I written by A.A. Gonchar 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 2013-11-11 with Mathematics categories.

A two-part volume containing a comprehensive description of the theory of entire and meromorphic functions of one complex variable and its applications, and a detailed review of recent investigations concerning the function-theoretical pecularities of polyanalytic functions (boundary behaviour, value distributions, degeneration, uniqueness etc).

Value Distribution Theory And Related Topics

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Author : Grigor A. Barsegian
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-02

Value Distribution Theory And Related Topics written by Grigor A. Barsegian 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 2006-05-02 with Mathematics categories.

The Nevanlinna theory of value distribution of meromorphic functions, one of the milestones of complex analysis during the last century, was c- ated to extend the classical results concerning the distribution of of entire functions to the more general setting of meromorphic functions. Later on, a similar reasoning has been applied to algebroid functions, subharmonic functions and meromorphic functions on Riemann surfaces as well as to - alytic functions of several complex variables, holomorphic and meromorphic mappings and to the theory of minimal surfaces. Moreover, several appli- tions of the theory have been exploited, including complex differential and functional equations, complex dynamics and Diophantine equations. The main emphasis of this collection is to direct attention to a number of recently developed novel ideas and generalizations that relate to the - velopment of value distribution theory and its applications. In particular, we mean a recent theory that replaces the conventional consideration of counting within a disc by an analysis of their geometric locations. Another such example is presented by the generalizations of the second main theorem to higher dimensional cases by using the jet theory. Moreover, s- ilar ideas apparently may be applied to several related areas as well, such as to partial differential equations and to differential geometry. Indeed, most of these applications go back to the problem of analyzing zeros of certain complex or real functions, meaning in fact to investigate level sets or level surfaces.

Value Distribution Of Meromorphic Functions

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Author : Anatoliĭ Asirovich Golʹdberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2008

Uniqueness Theory Of Meromorphic Functions

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Author : Chung-Chun Yang
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-10-04

Uniqueness Theory Of Meromorphic Functions written by Chung-Chun Yang 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 2004-10-04 with Mathematics categories.

This book is the first monograph in the field of uniqueness theory of meromorphic functions dealing with conditions under which there is the unique function satisfying given hypotheses. Developed by R. Nevanlinna, a Finnish mathematician, early in the 1920's, research in the field has developed rapidly over the past three decades with a great deal of fruitful results. This book systematically summarizes the most important results in the field, including many of the authors' own previously unpublished results. In addition, useful skills and simple proofs are introduced. This book is suitable for higher level and graduate students who have a basic grounding in complex analysis, but will also appeal to researchers in mathematics.

On The Value Distribution Of Meromorphic Functions With Their Derivatives

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