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Normal Families Of Meromorphic Functions
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Book Synopsis Normal Families of Meromorphic Functions by : Chi-Tai Chuang
Download or read book Normal Families of Meromorphic Functions written by Chi-Tai Chuang and published by World Scientific. This book was released on 1993 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents in a clear and systematic manner the general theory of normal families, quasi-normal families and Qm-normal families of meromorphic functions, and various applications. Much of this book contains results of the author's research, among them is the notion of m-normality which includes the classical notions of normality and quasi-normality introduced by Montel as particular cases. In this book, the notion of closed families of meromorphic functions is also introduced. In addition, applications concerning the existence of the solution of various extremal problems for certain classes of univalent or multivalent functions can also be found.
Download or read book Normal Families written by Joel L. Schiff and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: A book on the subject of normal families more than sixty years after the publication of Montel's treatise Ler;ons sur les familles normales de fonc tions analytiques et leurs applications is certainly long overdue. But, in a sense, it is almost premature, as so much contemporary work is still being produced. To misquote Dickens, this is the best of times, this is the worst of times. The intervening years have seen developments on a broad front, many of which are taken up in this volume. A unified treatment of the classical theory is also presented, with some attempt made to preserve its classical flavour. Since its inception early this century the notion of a normal family has played a central role in the development of complex function theory. In fact, it is a concept lying at the very heart of the subject, weaving a line of thought through Picard's theorems, Schottky's theorem, and the Riemann mapping theorem, to many modern results on meromorphic functions via the Bloch principle. It is this latter that has provided considerable impetus over the years to the study of normal families, and continues to serve as a guiding hand to future work. Basically, it asserts that a family of analytic (meromorphic) functions defined by a particular property, P, is likely to be a normal family if an entire (meromorphic in
Book Synopsis Normal Families and Normal Functions by : Peter V. Dovbush
Download or read book Normal Families and Normal Functions written by Peter V. Dovbush and published by CRC Press. This book was released on 2024-02-27 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book centers on normal families of holomorphic and meromorphic functions and also normal functions. The authors treat one complex variable, several complex variables, and infinitely many complex variables (i.e., Hilbert space). The theory of normal families is more than 100 years old. It has played a seminal role in the function theory of complex variables. It was used in the first rigorous proof of the Riemann mapping theorem. It is used to study automorphism groups of domains, geometric analysis, and partial differential equations. The theory of normal families led to the idea, in 1957, of normal functions as developed by Lehto and Virtanen. This is the natural class of functions for treating the Lindelof principle. The latter is a key idea in the boundary behavior of holomorphic functions. This book treats normal families, normal functions, the Lindelof principle, and other related ideas. Both the analytic and the geometric approaches to the subject area are offered. The authors include many incisive examples. The book could be used as the text for a graduate research seminar. It would also be useful reading for established researchers and for budding complex analysts.
Book Synopsis Value Distribution of Meromorphic Functions by : Jianhua Zheng
Download or read book Value Distribution of Meromorphic Functions written by Jianhua Zheng and published by Springer Science & Business Media. This book was released on 2011-03-31 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.
Book Synopsis Families of Meromorphic Functions on Compact Riemann Surfaces by : M. Namba
Download or read book Families of Meromorphic Functions on Compact Riemann Surfaces written by M. Namba and published by Springer. This book was released on 2006-11-15 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Normal Families Of Meromorphic Functions by : Qitai Zhuang
Download or read book Normal Families Of Meromorphic Functions written by Qitai Zhuang and published by World Scientific. This book was released on 1993-04-27 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents in a clear and systematic manner the general theory of normal families, quasi-normal families and Qm-normal families of meromorphic functions, and various applications. Much of this book contains results of the author's research, among them is the notion of Qm-normality which includes the classical notions of normality and quasi-normality introduced by Montel as particular cases. In this book, the notion of closed families of meromorphic functions is also introduced. In addition, applications concerning the existence of the solution of various extremal problems for certain classes of univalent or multivalent functions can also be found.
Book Synopsis Entire and Meromorphic Functions by : Lee A. Rubel
Download or read book Entire and Meromorphic Functions written by Lee A. Rubel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is a beautiful subject, and entire functions is its most beautiful branch. Every aspect of mathematics enters into it, from analysis, algebra, and geometry all the way to differential equations and logic. For example, my favorite theorem in all of mathematics is a theorem of R. NevanJinna that two functions, meromorphic in the whole complex plane, that share five values must be identical. For real functions, there is nothing that even remotely corresponds to this. This book is an introduction to the theory of entire and meromorphic functions, with a heavy emphasis on Nevanlinna theory, otherwise known as value-distribution theory. Things included here that occur in no other book (that we are aware of) are the Fourier series method for entire and mero morphic functions, a study of integer valued entire functions, the Malliavin Rubel extension of Carlson's Theorem (the "sampling theorem"), and the first-order theory of the ring of all entire functions, and a final chapter on Tarski's "High School Algebra Problem," a topic from mathematical logic that connects with entire functions. This book grew out of a set of classroom notes for a course given at the University of Illinois in 1963, but they have been much changed, corrected, expanded, and updated, partially for a similar course at the same place in 1993. My thanks to the many students who prepared notes and have given corrections and comments.
Book Synopsis Nevanlinna Theory, Normal Families, and Algebraic Differential Equations by : Norbert Steinmetz
Download or read book Nevanlinna Theory, Normal Families, and Algebraic Differential Equations written by Norbert Steinmetz and published by Springer. This book was released on 2017-07-24 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a modern introduction to Nevanlinna theory and its intricate relation to the theory of normal families, algebraic functions, asymptotic series, and algebraic differential equations. Following a comprehensive treatment of Nevanlinna’s theory of value distribution, the author presents advances made since Hayman’s work on the value distribution of differential polynomials and illustrates how value- and pair-sharing problems are linked to algebraic curves and Briot–Bouquet differential equations. In addition to discussing classical applications of Nevanlinna theory, the book outlines state-of-the-art research, such as the effect of the Yosida and Zalcman–Pang method of re-scaling to algebraic differential equations, and presents the Painlevé–Yosida theorem, which relates Painlevé transcendents and solutions to selected 2D Hamiltonian systems to certain Yosida classes of meromorphic functions. Aimed at graduate students interested in recent developments in the field and researchers working on related problems, Nevanlinna Theory, Normal Families, and Algebraic Differential Equations will also be of interest to complex analysts looking for an introduction to various topics in the subject area. With examples, exercises and proofs seamlessly intertwined with the body of the text, this book is particularly suitable for the more advanced reader.
Book Synopsis Fix-points And Factorization Of Meromorphic Functions: Topics In Complex Analysis by : Chung-chun Yang
Download or read book Fix-points And Factorization Of Meromorphic Functions: Topics In Complex Analysis written by Chung-chun Yang and published by World Scientific. This book was released on 1990-01-01 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Complex Analysis by : Theodore W. Gamelin
Download or read book Complex Analysis written by Theodore W. Gamelin and published by Springer Science & Business Media. This book was released on 2013-11-01 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to complex analysis for students with some knowledge of complex numbers from high school. It contains sixteen chapters, the first eleven of which are aimed at an upper division undergraduate audience. The remaining five chapters are designed to complete the coverage of all background necessary for passing PhD qualifying exams in complex analysis. Topics studied include Julia sets and the Mandelbrot set, Dirichlet series and the prime number theorem, and the uniformization theorem for Riemann surfaces, with emphasis placed on the three geometries: spherical, euclidean, and hyperbolic. Throughout, exercises range from the very simple to the challenging. The book is based on lectures given by the author at several universities, including UCLA, Brown University, La Plata, Buenos Aires, and the Universidad Autonomo de Valencia, Spain.
Book Synopsis Meromorphic Functions over non-Archimedean Fields by : Pei-Chu Hu
Download or read book Meromorphic Functions over non-Archimedean Fields written by Pei-Chu Hu and published by Springer Science & Business Media. This book was released on 2000-09-30 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces value distribution theory over non-Archimedean fields, starting with a survey of two Nevanlinna-type main theorems and defect relations for meromorphic functions and holomorphic curves. Secondly, it gives applications of the above theory to, e.g., abc-conjecture, Waring's problem, uniqueness theorems for meromorphic functions, and Malmquist-type theorems for differential equations over non-Archimedean fields. Next, iteration theory of rational and entire functions over non-Archimedean fields and Schmidt's subspace theorems are studied. Finally, the book suggests some new problems for further research. Audience: This work will be of interest to graduate students working in complex or diophantine approximation as well as to researchers involved in the fields of analysis, complex function theory of one or several variables, and analytic spaces.
Book Synopsis Meromorphic Functions by : Walter Kurt Hayman
Download or read book Meromorphic Functions written by Walter Kurt Hayman and published by . This book was released on 1964 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fix-points and Factorization of Meromorphic Functions by : Qitai Zhuang
Download or read book Fix-points and Factorization of Meromorphic Functions written by Qitai Zhuang and published by World Scientific. This book was released on 1990 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Factorization of Meromorphic Functions by : Fred Gross
Download or read book Factorization of Meromorphic Functions written by Fred Gross and published by . This book was released on 1973 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Complex Analysis by : Mario Gonzalez
Download or read book Complex Analysis written by Mario Gonzalez and published by Routledge. This book was released on 2018-03-09 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: A selection of some important topics in complex analysis, intended as a sequel to the author's Classical complex analysis (see preceding entry). The five chapters are devoted to analytic continuation; conformal mappings, univalent functions, and nonconformal mappings; entire function; meromorphic fu
Book Synopsis Value Distribution of Meromorphic Functions by : Anatoliĭ Asirovich Golʹdberg
Download or read book Value Distribution of Meromorphic Functions written by Anatoliĭ Asirovich Golʹdberg and published by American Mathematical Soc.. This book was released on 2008 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.
Book Synopsis Proceedings of the International Symposium/Workshop on Geometric Study of Foliations by : Tadayoshi Mizutani
Download or read book Proceedings of the International Symposium/Workshop on Geometric Study of Foliations written by Tadayoshi Mizutani and published by World Scientific. This book was released on 1994 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt:
