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## Function Theory of One Complex Variable

- Author : Robert Everist Greene,Steven George Krantz
- Publisher :
- Release Date :2006
- Total pages :504
- ISBN : 9780821839621

**Summary :** Complex analysis is one of the most central subjects in mathematics. It is compelling and rich in its own right, but it is also remarkably useful in a wide variety of other mathematical subjects, both pure and applied. This book is different from others in that it treats complex variables as a direct development from multivariable real calculus. As each new idea is introduced, it is related to the corresponding idea from real analysis and calculus. The text is rich with examples and exercises that illustrate this point. The authors have systematically separated the analysis from the topology, as can be seen in their proof of the Cauchy theorem. The book concludes with several chapters on special topics, including full treatments of special functions, the prime number theorem, and the Bergman kernel. The authors also treat $H^p$ spaces and Painleve's theorem on smoothness to the boundary for conformal maps. This book is a text for a first-year graduate course in complex analysis. It is an engaging and modern introduction to the subject, reflecting the authors' expertise both as mathematicians and as expositors.

## Functions of One Complex Variable I

- Author : John B. Conway
- Publisher :
- Release Date :1978-08-24
- Total pages :317
- ISBN : 9780387903286

**Summary :** This book is intended as a textbook for a first course in the theory of functions of one complex variable for students who are mathematically mature enough to understand and execute E - 8 arguments. The actual pre requisites for reading this book are quite minimal; not much more than a stiff course in basic calculus and a few facts about partial derivatives. The topics from advanced calculus that are used (e.g., Leibniz's rule for differ entiating under the integral sign) are proved in detail. Complex Variables is a subject which has something for all mathematicians. In addition to having applications to other parts of analysis, it can rightly claim to be an ancestor of many areas of mathematics (e.g., homotopy theory, manifolds). This view of Complex Analysis as "An Introduction to Mathe matics" has influenced the writing and selection of subject matter for this book. The other guiding principle followed is that all definitions, theorems, etc.

## Function Theory of One Complex Variable

- Author : Robert E. Greene,Steven G. Krantz
- Publisher :
- Release Date :1997-04-25
- Total pages :496
- ISBN :

**Summary :** This volume connects complex analysis with calculus, algebra, geometry, topology and analysis. Exercises and illustrations are provided throughout the text. Also included is information on Bergman Kernal and two boundary behaviour of conformal mappings.

## Functions of One Complex Variable

- Author : J.B. Conway
- Publisher :
- Release Date :2012-12-06
- Total pages :313
- ISBN : 1461599725

**Summary :** This book is intended as a textbook for a first course in the theory of functions of one complex variable for students who are mathematically mature enough to understand and execute E - I) arguments. The actual pre requisites for reading this book are quite minimal; not much more than a stiff course in basic calculus and a few facts about partial derivatives. The topics from advanced calculus that are used (e.g., Leibniz's rule for differ entiating under the integral sign) are proved in detail. Complex Variables is a subject which has something for all mathematicians. In addition to having applications to other parts of analysis, it can rightly claim to be an ancestor of many areas of mathematics (e.g., homotopy theory, manifolds). This view of Complex Analysis as "An Introduction to Mathe matics" has influenced the writing and selection of subject matter for this book. The other guiding principle followed is that all definitions, theorems, etc.

## Function Theory of One Complex Variable

- Author : Robert Everist Greene,Steven George Krantz
- Publisher :
- Release Date :2002
- Total pages :502
- ISBN : 9780821829059

**Summary :** Complex analysis is one of the most beautiful subjects that we learn as graduate students. Part of the joy comes from being able to arrive quickly at some real theorems. The fundamental techniques of complex variables are also used to solve real problems in neighbouring subjects, such as number theory or PDEs.

## Function Theory of One Complex Variable

- Author : Robert Everist Greene,Steven George Krantz
- Publisher :
- Release Date :2002
- Total pages :502
- ISBN : 9780821829059

**Summary :** Complex analysis is one of the most beautiful subjects that we learn as graduate students. Part of the joy comes from being able to arrive quickly at some real theorems. The fundamental techniques of complex variables are also used to solve real problems in neighbouring subjects, such as number theory or PDEs.

## Analytic Function Theory of One Complex Variable

- Author : Yūsaku Komatsu,Kiyoshi Niino,Chung-Chun Yang
- Publisher :
- Release Date :1989
- Total pages :392
- ISBN : 9780582037809

**Summary :**

## Elementary Theory of Analytic Functions of One or Several Complex Variables

- Author : Henri Cartan
- Publisher :
- Release Date :2013-04-22
- Total pages :228
- ISBN : 0486318672

**Summary :** Basic treatment includes existence theorem for solutions of differential systems where data is analytic, holomorphic functions, Cauchy's integral, Taylor and Laurent expansions, more. Exercises. 1973 edition.

## Geometric Theory of Functions of a Complex Variable

- Author : Gennadiĭ Mikhaĭlovich Goluzin
- Publisher :
- Release Date :1969
- Total pages :676
- ISBN : 9780821886557

**Summary :**

## Functions of One Complex Variable II

- Author : John B. Conway
- Publisher :
- Release Date :2012-12-06
- Total pages :396
- ISBN : 1461208173

**Summary :** This book discusses a variety of problems which are usually treated in a second course on the theory of functions of one complex variable, the level being gauged for graduate students. It treats several topics in geometric function theory as well as potential theory in the plane, covering in particular: conformal equivalence for simply connected regions, conformal equivalence for finitely connected regions, analytic covering maps, de Branges' proof of the Bieberbach conjecture, harmonic functions, Hardy spaces on the disk, potential theory in the plane. A knowledge of integration theory and functional analysis is assumed.

## Complex Analysis

- Author : Murali Rao,Henrik Stetkr
- Publisher :
- Release Date :1991
- Total pages :240
- ISBN : 9789810203757

**Summary :** This is a rigorous introduction to the theory of complex functions of one complex variable. The authors have made an effort to present some of the deeper and more interesting results, for example, Picard's theorems, Riemann mapping theorem, Runge's theorem in the first few chapters. However, the very basic theory is nevertheless given a thorough treatment so that readers should never feel lost. After the first five chapters, the order may be adapted to suit the course. Each chapter finishes with exercises.

## Function Theory of Several Complex Variables

- Author : Steven George Krantz
- Publisher :
- Release Date :2001
- Total pages :564
- ISBN : 0821827243

**Summary :** The theory of several complex variables can be studied from several different perspectives. In this book, Steven Krantz approaches the subject from the point of view of a classical analyst, emphasizing its function-theoretic aspects. He has taken particular care to write the book with the student in mind, with uniformly extensive and helpful explanations, numerous examples, and plentiful exercises of varying difficulty. In the spirit of a student-oriented text, Krantz begins with an introduction to the subject, including an insightful comparison of analysis of several complex variables with the more familiar theory of one complex variable. The main topics in the book include integral formulas, convexity and pseudoconvexity, methods from harmonic analysis, and several aspects of the $\overline{\partial}$ problem. Some further topics are zero sets of holomorphic functions, estimates, partial differential equations, approximation theory, the boundary behavior of holomorphic functions, inner functions, invariant metrics, and holomorphic mappings. While due attention is paid to algebraic aspects of several complex variables (sheaves, Cousin problems, etc.), the student with a background in real and complex variable theory, harmonic analysis, and differential equations will be most comfortable with this treatment. This book is suitable for a first graduate course in several complex variables.

## Topics in the Theory of Functions of One Complex Variable

- Author : W. H. J. Fuchs,Alan Schumitzky
- Publisher :
- Release Date :1967
- Total pages :193
- ISBN :

**Summary :**

## Analytic Functions of Several Complex Variables

- Author : Robert Clifford Gunning,Hugo Rossi
- Publisher :
- Release Date :2009
- Total pages :317
- ISBN : 0821821652

**Summary :** The theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century. After initial successes by Poincare and others in the late 19th and early 20th centuries, the theory encountered obstacles that prevented it from growing quickly into an analogue of the theory for functions of one complex variable. Beginning in the 1930s, initially through the work of Oka, then H. Cartan, and continuing with the work of Grauert, Remmert, and others, new tools were introduced into the theory of several complex variables that resolved many of the open problems and fundamentally changed the landscape of the subject. These tools included a central role for sheaf theory and increased uses of topology and algebra. The book by Gunning and Rossi was the first of the modern era of the theory of several complex variables, which is distinguished by the use of these methods. The intention of Gunning and Rossi's book is to provide an extensive introduction to the Oka-Cartan theory and some of its applications, and to the general theory of analytic spaces. Fundamental concepts and techniques are discussed as early as possible. The first chapter covers material suitable for a one-semester graduate course, presenting many of the central problems and techniques, often in special cases. The later chapters give more detailed expositions of sheaf theory for analytic functions and the theory of complex analytic spaces. Since its original publication, this book has become a classic resource for the modern approach to functions of several complex variables and the theory of analytic spaces. Further information about this book, including updates, can be found at the following URL: www.ams.org/bookpages/chel-368.

## Theory of Functions of a Complex Variable

- Author : C. Caratheodory
- Publisher :
- Release Date :2001
- Total pages :304
- ISBN : 0821828312

**Summary :** This book is a translation by F. Steinhardt of the last of Caratheodory's celebrated text books, Funktiontheorie, Volume 1.