Nevanlinna Theory Normal Families And Algebraic Differential Equations
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Nevanlinna Theory Normal Families And Algebraic Differential Equations
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Author : Norbert Steinmetz
language : en
Publisher: Springer
Release Date : 2017-07-24
Nevanlinna Theory Normal Families And Algebraic Differential Equations written by Norbert Steinmetz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-24 with Mathematics categories.
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.
Nevanlinna Theory And Complex Differential Equations
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Author : Ilpo Laine
language : en
Publisher: Walter de Gruyter
Release Date : 2011-06-01
Nevanlinna Theory And Complex Differential Equations written by Ilpo Laine and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-01 with Mathematics categories.
The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.
Normal Families And Normal Functions
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Author : Peter V. Dovbush
language : en
Publisher: CRC Press
Release Date : 2024-02-27
Normal Families And Normal Functions written by Peter V. Dovbush and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-27 with Mathematics categories.
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.
Current Trends In Analysis Its Applications And Computation
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Author : Paula Cerejeiras
language : en
Publisher: Springer Nature
Release Date : 2022-10-03
Current Trends In Analysis Its Applications And Computation written by Paula Cerejeiras and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-03 with Mathematics categories.
This volume contains the contributions of the participants of the 12th ISAAC congress which was held at the University of Aveiro, Portugal, from July 29 to August 3, 2019. These contributions originate from the following sessions: Applications of dynamical systems theory in biology, Complex Analysis and Partial Differential Equations, Complex Geometry, Complex Variables and Potential Theory, Constructive Methods in the Theory of Composite and Porous Media, Function Spaces and Applications, Generalized Functions and Applications, Geometric & Regularity Properties of Solutions to Elliptic and Parabolic PDEs, Geometries Defined by Differential Forms, Partial Differential Equations on Curved Spacetimes, Partial Differential Equations with Nonstandard Growth, Quaternionic and Clifford Analysis, Recent Progress in Evolution Equations, Wavelet theory and its Related Topics.
Nevanlinna Theory And Its Relation To Diophantine Approximation
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Author : Min Ru
language : en
Publisher: World Scientific
Release Date : 2001-06-06
Nevanlinna Theory And Its Relation To Diophantine Approximation written by Min Ru and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-06 with Mathematics categories.
It was discovered recently that Nevanlinna theory and Diophantine approximation bear striking similarities and connections. This book provides an introduction to both Nevanlinna theory and Diophantine approximation, with emphasis on the analogy between these two subjects.Each chapter is divided into part A and part B. Part A deals with Nevanlinna theory and part B covers Diophantine approximation. At the end of each chapter, a table is provided to indicate the correspondence of theorems.
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.
Normal Families
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Author : Joel L. Schiff
language : en
Publisher:
Release Date : 1993
Normal Families written by Joel L. Schiff and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
This is the first book devoted solely to the subject of normal families of analytic and meromorphic functions since the 1927 treatise of Paul Montel. A considerable body of research has evolved since then, and this text provides a comprehensive treatment of the entire theory. 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, the Riemann mapping theorem, to many modern results on meromorphic functions via the Bloch principle. It is this latter which has provided considerable impetus over the years to the study of normal families, and continues to serve as a guiding hand to future work. Numerous applications of the normal family theory are discussed, particularly those found in the study of extremal problems, normal functions, harmonic functions, discontinuous groups, and complex dynamical systems. Only a basic knowledge of complex analysis and topology is assumed. All other necessary material for the study of the subject is included in the first chapter. The scope of the book ranges from advanced undergraduate to research level.
Applications Of Lie S Theory Of Ordinary And Partial Differential Equations
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Author : L Dresner
language : en
Publisher: CRC Press
Release Date : 1998-01-01
Applications Of Lie S Theory Of Ordinary And Partial Differential Equations written by L Dresner and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Science categories.
Lie's group theory of differential equations unifies the many ad hoc methods known for solving differential equations and provides powerful new ways to find solutions. The theory has applications to both ordinary and partial differential equations and is not restricted to linear equations. Applications of Lie's Theory of Ordinary and Partial Differential Equations provides a concise, simple introduction to the application of Lie's theory to the solution of differential equations. The author emphasizes clarity and immediacy of understanding rather than encyclopedic completeness, rigor, and generality. This enables readers to quickly grasp the essentials and start applying the methods to find solutions. The book includes worked examples and problems from a wide range of scientific and engineering fields.
Proceedings Of The Second Isaac Congress
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Author : Heinrich G.W. Begehr
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Proceedings Of The Second Isaac Congress written by Heinrich G.W. Begehr 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 2013-12-01 with Mathematics categories.
This book is the Proceedings of the Second ISAAC Congress. ISAAC is the acronym of the International Society for Analysis, its Applications and Computation. The president of ISAAC is Professor Robert P. Gilbert, the second named editor of this book, e-mail: gilbert@math.udel.edu. The Congress is world-wide valued so highly that an application for a grant has been selected and this project has been executed with Grant No. 11-56 from *the Commemorative Association for the Japan World Exposition (1970). The finance of the publication of this book is exclusively the said Grant No. 11-56 from *. Thus, a pair of each one copy of two volumes of this book will be sent to all contributors, who registered at the Second ISAAC Congress in Fukuoka, free of charge by the Kluwer Academic Publishers. Analysis is understood here in the broad sense of the word, includ ing differential equations, integral equations, functional analysis, and function theory. It is the purpose of ISAAC to promote analysis, its applications, and its interaction with computation. With this objective, ISAAC organizes international Congresses for the presentation and dis cussion of research on analysis. ISAAC welcomes new members and those interested in joining ISAAC are encouraged to look at the web site http://www .math. udel.edu/ gilbert/isaac/index.html vi and http://www.math.fu-berlin.de/ rd/ ag/isaac/newton/index.html.
Finite Or Infinite Dimensional Complex Analysis And Applications
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Author : Le Hung Son
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Finite Or Infinite Dimensional Complex Analysis And Applications written by Le Hung Son 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 2013-12-01 with Mathematics categories.
There is almost no field in Mathematics which does not use Mathe matical Analysis. Computer methods in Applied Mathematics, too, are often based on statements and procedures of Mathematical Analysis. An important part of Mathematical Analysis is Complex Analysis because it has many applications in various branches of Mathematics. Since the field of Complex Analysis and its applications is a focal point in the Vietnamese research programme, the Hanoi University of Technology organized an International Conference on Finite or Infinite Dimensional Complex Analysis and Applications which took place in Hanoi from August 8 - 12, 2001. This conference th was the 9 one in a series of conferences which take place alternately in China, Japan, Korea and Vietnam each year. The first one took place th at Pusan University in Korea in 1993. The preceding 8 conference was th held in Shandong in China in August 2000. The 9 conference of the was the first one which took place above mentioned series of conferences in Vietnam. Present trends in Complex Analysis reflected in the present volume are mainly concentrated in the following four research directions: 1 Value distribution theory (including meromorphic funtions, mero morphic mappings, as well as p-adic functions over fields of finite or zero characteristic) and its applications, 2 Holomorphic functions in several (finitely or infinitely many) com plex variables, 3 Clifford Analysis, i.e., complex methods in higher-dimensional real Euclidian spaces, 4 Generalized analytic functions.