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Theory Of Entire And Meromorphic Functions
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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 Uniqueness Theory of Meromorphic Functions by : Chung-Chun Yang
Download or read book Uniqueness Theory of Meromorphic Functions written by Chung-Chun Yang and published by Springer Science & Business Media. This book was released on 2004-10-04 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Theory of Entire and Meromorphic Functions by : Guan-hou Zhang
Download or read book Theory of Entire and Meromorphic Functions written by Guan-hou Zhang and published by American Mathematical Soc.. This book was released on 1993-01-01 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book was originally written in Chinese in 1986 by the noted complex analyst Zhang Guan-Hou, who was a research fellow at the Academia Sinica. The book provides a basic introduction to the development of the theory of entire and meromorphic functions from the 1950s to the early 1980s. After an opening chapter introducing fundamentals of Nevanlinna's value distribution theory, this book discusses various relationships among and developments of three central concepts: deficient value, asymptotic value, and singular direction. This book describes many significant results and research directions developed by Zhang and other Chinese complex analysts and published in Chinese mathematical journals. A comprehensive and self-contained reference, this book is useful for graduate students and researchers in complex analysis.
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 Theory of Entire and Meromorphic Functions by : Guan-Hou Zhang
Download or read book Theory of Entire and Meromorphic Functions written by Guan-Hou Zhang and published by American Mathematical Soc.. This book was released on 1993 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book was originally written in Chinese in 1986 by the noted complex analyst Zhang Guan-Hou, who was a research fellow at the Academia Sinica. The book provides a basic introduction to the development of the theory of entire and meromorphic functions from the 1950s to the early 1980s. After an opening chapter introducing fundamentals of Nevanlinna's value distribution theory, this book discusses various relationships among and developments of three central concepts: deficient value, asymptotic value, and singular direction. This book describes many significant results and research directions developed by Zhang and other Chinese complex analysts and published in Chinese mathematical journals. A comprehensive and self-contained reference, this book is useful for graduate students and researchers in complex analysis.
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 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 Introduction to the Theory of Entire Functions by :
Download or read book Introduction to the Theory of Entire Functions written by and published by Academic Press. This book was released on 1974-02-08 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to the Theory of Entire Functions
Book Synopsis Nevanlinna Theory in Several Complex Variables and Diophantine Approximation by : Junjiro Noguchi
Download or read book Nevanlinna Theory in Several Complex Variables and Diophantine Approximation written by Junjiro Noguchi and published by Springer Science & Business Media. This book was released on 2013-12-09 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to provide a comprehensive account of higher dimensional Nevanlinna theory and its relations with Diophantine approximation theory for graduate students and interested researchers. This book with nine chapters systematically describes Nevanlinna theory of meromorphic maps between algebraic varieties or complex spaces, building up from the classical theory of meromorphic functions on the complex plane with full proofs in Chap. 1 to the current state of research. Chapter 2 presents the First Main Theorem for coherent ideal sheaves in a very general form. With the preparation of plurisubharmonic functions, how the theory to be generalized in a higher dimension is described. In Chap. 3 the Second Main Theorem for differentiably non-degenerate meromorphic maps by Griffiths and others is proved as a prototype of higher dimensional Nevanlinna theory. Establishing such a Second Main Theorem for entire curves in general complex algebraic varieties is a wide-open problem. In Chap. 4, the Cartan-Nochka Second Main Theorem in the linear projective case and the Logarithmic Bloch-Ochiai Theorem in the case of general algebraic varieties are proved. Then the theory of entire curves in semi-abelian varieties, including the Second Main Theorem of Noguchi-Winkelmann-Yamanoi, is dealt with in full details in Chap. 6. For that purpose Chap. 5 is devoted to the notion of semi-abelian varieties. The result leads to a number of applications. With these results, the Kobayashi hyperbolicity problems are discussed in Chap. 7. In the last two chapters Diophantine approximation theory is dealt with from the viewpoint of higher dimensional Nevanlinna theory, and the Lang-Vojta conjecture is confirmed in some cases. In Chap. 8 the theory over function fields is discussed. Finally, in Chap. 9, the theorems of Roth, Schmidt, Faltings, and Vojta over number fields are presented and formulated in view of Nevanlinna theory with results motivated by those in Chaps. 4, 6, and 7.
Book Synopsis Complex Analysis I by : A.A. Gonchar
Download or read book Complex Analysis I written by A.A. Gonchar and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
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 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 I by : A.A. Gonchar
Download or read book Complex Analysis I written by A.A. Gonchar and published by Springer. This book was released on 2012-11-30 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Book Synopsis Meromorphic Functions and Linear Algebra by : Olavi Nevanlinna
Download or read book Meromorphic Functions and Linear Algebra written by Olavi Nevanlinna and published by American Mathematical Soc.. This book was released on 2003 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume describes for the first time in monograph form important applications in numerical methods of linear algebra. The author presents new material and extended results from recent papers in a very readable style. The main goal of the book is to study the behavior of the resolvent of a matrix under the perturbation by low rank matrices. Whereas the eigenvalues (the poles of the resolvent) and the pseudospectra (the sets where the resolvent takes large values) can move dramatically under such perturbations, the growth of the resolvent as a matrix-valued meromorphic function remains essentially unchanged. This has practical implications to the analysis of iterative solvers for large systems of linear algebraic equations. First, the book introduces the basics of value distribution theory of meromorphic scalar functions. It then introduces a new nonlinear tool for linear algebra, the total logarithmic size of a matrix, which allows for a nontrivial generalization of Rolf Nevanlinna's characteristic function from the scalar theory to matrix- and operator-valued functions. In particular, the theory of perturbations by low rank matrices becomes possible. As an example, if the spectrum of a normal matrix collapses under a low rank perturbation, there is always a compensation in terms of the loss of orthogonality of the eigenvectors. This qualitative phenomenon is made quantitative by using the new tool. Applications are given to rational approximation, to the Kreiss matrix theorem, and to convergence of Krylov solvers. The book is intended for researchers in mathematics in general and especially for those working in numerical linear algebra. Much of the book is understandable if the reader has a good background in linear algebra and a first course in complex analysis.
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 Analytic Function Theory by : Einar Hille
Download or read book Analytic Function Theory written by Einar Hille and published by American Mathematical Soc.. This book was released on 2002 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emphasizes the conceptual and historical continuity of analytic function theory. This work covers topics including elliptic functions, entire and meromorphic functions, as well as conformal mapping. It features chapters on majorization and on functions holomorphic in a half-plane.
Book Synopsis Nevanlinna’s Theory of Value Distribution by : William Cherry
Download or read book Nevanlinna’s Theory of Value Distribution written by William Cherry and published by Springer Science & Business Media. This book was released on 2001-04-24 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph serves as a self-contained introduction to Nevanlinna's theory of value distribution as well as a valuable reference for research specialists. Authors present, for the first time in book form, the most modern and refined versions of the Second Main Theorem with precise error terms, in both the geometric and logarithmic derivative based approaches. A unique feature of the monograph is its number theoretic digressions These special sections assume no background in number theory and explore the exciting interconnections between Nevanlinna theory and the theory of Diophantine approximation.
