Complex Analysis in One Variable

Author: Raghavan Narasimhan,Yves Nievergelt

Publisher: Springer Science & Business Media

ISBN: 1461201756

Category: Mathematics

Page: 381

View: 3343

The original edition of this book has been out of print for some years. The appear ance of the present second edition owes much to the initiative of Yves Nievergelt at Eastern Washington University, and the support of Ann Kostant, Mathematics Editor at Birkhauser. Since the book was first published, several people have remarked on the absence of exercises and expressed the opinion that the book would have been more useful had exercises been included. In 1997, Yves Nievergelt informed me that, for a decade, he had regularly taught a course at Eastern Washington based on the book, and that he had systematically compiled exercises for his course. He kindly put his work at my disposal. Thus, the present edition appears in two parts. The first is essentially just a reprint of the original edition. I have corrected the misprints of which I have become aware (including those pointed out to me by others), and have made a small number of other minor changes.
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A Course in Complex Analysis in One Variable

Author: Martin A. Moskowitz

Publisher: World Scientific

ISBN: 9789810247805

Category: Mathematics

Page: 149

View: 2925

Organized in an especially efficient manner, presenting basic complex analysis. Includes about 50 exercises
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Funktionentheorie

Author: Reinhold Remmert

Publisher: N.A

ISBN: 9783540553847

Category: Functions of complex variables

Page: 299

View: 5212

Diese dritte Auflage wurde zusammen mit dem zweitgenannten Autor kritisch durchgesehen, ergnzt und verbessert. Ein weiteres Kapitel ber geometrische Funktionentheorie und schlichte Funktionen enthlt einen Beweis der Bieberbachschen Vermutung. Der ... vorliegende zweite Band der Funktionentheorie erfllt voll die Erwartungen, die der erste Band geweckt hat. Wieder beeindrucken vor allem die hochinteressanten historischen Bemerkungen zu den einzelnen Themenkreisen, als besonderer Leckerbissen wird das Gutachten von Gau ber Riemanns Dissertation vorgestellt... Jedes einzelne Kapitel enthlt ausfhrliche Literaturangaben. Ferner werden oft sehr aufschlussreiche Hinweise auf die Funktionentheorie mehrerer Vernderlicher gegeben. Die vielen Beispiele und bungsaufgaben bilden eine wertvolle Ergnzung der brillant dargelegten Theorie. Der Rezensent bedauert, dass ihm nicht schon als Student ein derartig umfassendes, qualitativ hochstehendes Lehrbuch zur Verfgung stand." Monatshefte fr Mathematik
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Function Theory of One Complex Variable

Author: Robert Everist Greene,Steven George Krantz

Publisher: American Mathematical Soc.

ISBN: 9780821839621

Category: Mathematics

Page: 504

View: 994

The third edition of this textbook on one of mathematics' most central subjects includes revisions of many exercises for greater consistency, as well as clarifications of several proofs. The authors treat complex variables as a direct development from calculus, relating ideas such as the complex derivative and the Cauchy theorem to their cognate idea from calculus. Many examples, figures and exercises enrich the text.
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Maß und Kategorie

Author: J.C. Oxtoby

Publisher: Springer-Verlag

ISBN: 364296074X

Category: Mathematics

Page: 112

View: 6624

Dieses Buch behandelt hauptsächlich zwei Themenkreise: Der Bairesche Kategorie-Satz als Hilfsmittel für Existenzbeweise sowie Die "Dualität" zwischen Maß und Kategorie. Die Kategorie-Methode wird durch viele typische Anwendungen erläutert; die Analogie, die zwischen Maß und Kategorie besteht, wird nach den verschiedensten Richtungen hin genauer untersucht. Hierzu findet der Leser eine kurze Einführung in die Grundlagen der metrischen Topologie; außerdem werden grundlegende Eigenschaften des Lebesgue schen Maßes hergeleitet. Es zeigt sich, daß die Lebesguesche Integrationstheorie für unsere Zwecke nicht erforderlich ist, sondern daß das Riemannsche Integral ausreicht. Weiter werden einige Begriffe aus der allgemeinen Maßtheorie und Topologie eingeführt; dies geschieht jedoch nicht nur der größeren Allgemeinheit wegen. Es erübrigt sich fast zu erwähnen, daß sich die Bezeichnung "Kategorie" stets auf "Bairesche Kategorie" be zieht; sie hat nichts zu tun mit dem in der homologischen Algebra verwendeten Begriff der Kategorie. Beim Leser werden lediglich grundlegende Kenntnisse aus der Analysis und eine gewisse Vertrautheit mit der Mengenlehre vorausgesetzt. Für die hier untersuchten Probleme bietet sich in natürlicher Weise die mengentheoretische Formulierung an. Das vorlie gende Buch ist als Einführung in dieses Gebiet der Analysis gedacht. Man könnte es als Ergänzung zur üblichen Grundvorlesung über reelle Analysis, als Grundlage für ein Se minar oder auch zum selbständigen Studium verwenden. Bei diesem Buch handelt es sich vorwiegend um eine zusammenfassende Darstellung; jedoch finden sich in ihm auch einige Verfeinerungen bekannter Resultate, namentlich Satz 15.6 und Aussage 20.4. Das Literaturverzeichnis erhebt keinen Anspruch auf Vollständigkeit. Häufig werden Werke zitiert, die weitere Literaturangaben enthalten.
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Carleman’s Formulas in Complex Analysis

Theory and Applications

Author: L.A. Aizenberg

Publisher: Springer Science & Business Media

ISBN: 9780792321217

Category: Mathematics

Page: 299

View: 9044

Integral representations of holomorphic functions play an important part in the classical theory of functions of one complex variable and in multidimensional com plex analysis (in the later case, alongside with integration over the whole boundary aD of a domain D we frequently encounter integration over the Shilov boundary 5 = S(D)). They solve the classical problem of recovering at the points of a do main D a holomorphic function that is sufficiently well-behaved when approaching the boundary aD, from its values on aD or on S. Alongside with this classical problem, it is possible and natural to consider the following one: to recover the holomorphic function in D from its values on some set MeaD not containing S. Of course, M is to be a set of uniqueness for the class of holomorphic functions under consideration (for example, for the functions continuous in D or belonging to the Hardy class HP(D), p ~ 1).
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Holomorphic Operator Functions of One Variable and Applications

Methods from Complex Analysis in Several Variables

Author: Israel Gohberg,Jürgen Leiterer

Publisher: Springer Science & Business Media

ISBN: 3034601263

Category: Mathematics

Page: 424

View: 1204

This book presents holomorphic operator functions of a single variable and applications, which are focused on the relations between local and global theories. It is based on methods and technics of complex analysis of several variables.
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Several Complex Variables and the Geometry of Real Hypersurfaces

Author: John P. D'Angelo

Publisher: CRC Press

ISBN: 9780849382727

Category: Mathematics

Page: 288

View: 4622

Several Complex Variables and the Geometry of Real Hypersurfaces covers a wide range of information from basic facts about holomorphic functions of several complex variables through deep results such as subelliptic estimates for the ?-Neumann problem on pseudoconvex domains with a real analytic boundary. The book focuses on describing the geometry of a real hypersurface in a complex vector space by understanding its relationship with ambient complex analytic varieties. You will learn how to decide whether a real hypersurface contains complex varieties, how closely such varieties can contact the hypersurface, and why it's important. The book concludes with two sets of problems: routine problems and difficult problems (many of which are unsolved). Principal prerequisites for using this book include a thorough understanding of advanced calculus and standard knowledge of complex analysis in one variable. Several Complex Variables and the Geometry of Real Hypersurfaces will be a useful text for advanced graduate students and professionals working in complex analysis.
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Einführung in die Komplexe Analysis

Elemente der Funktionentheorie

Author: Wolfgang Fischer,Ingo Lieb

Publisher: Springer-Verlag

ISBN: 3834893773

Category: Mathematics

Page: 214

View: 7408

In den Bachelor-Studiengängen der Mathematik steht für die Komplexe Analysis (Funktionentheorie) oft nur eine einsemestrige 2-stündige Vorlesung zur Verfügung. Dieses Buch eignet sich als Grundlage für eine solche Vorlesung im 2. Studienjahr. Mit einer guten thematischen Auswahl, vielen Beispielen und ausführlichen Erläuterungen gibt dieses Buch eine Darstellung der Komplexen Analysis, die genau die Grundlagen und den wesentlichen Kernbestand dieses Gebietes enthält. Das Buch bietet über diese Grundausbildung hinaus weiteres Lehrmaterial als Ergänzung, sodass es auch für eine 3- oder 4 –stündige Vorlesung geeignet ist. Je nach Hörerkreis kann der Stoff unterschiedlich erweitert werden. So wurden für den „Bachelor Lehramt“ die geometrischen Aspekte der Komplexen Analysis besonders herausgearbeitet.
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Complex Analysis

Author: Eberhard Freitag,Rolf Busam

Publisher: Springer Science & Business Media

ISBN: 3540939830

Category: Mathematics

Page: 532

View: 3547

All needed notions are developed within the book: with the exception of fundamentals which are presented in introductory lectures, no other knowledge is assumed Provides a more in-depth introduction to the subject than other existing books in this area Over 400 exercises including hints for solutions are included
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Complex Analysis in Banach Spaces

Holomorphic Functions and Domains of Holomorphy in Finite and Infinite Dimensions

Author: J. Mujica

Publisher: Elsevier

ISBN: 9780080872315

Category: Mathematics

Page: 433

View: 3748

Problems arising from the study of holomorphic continuation and holomorphic approximation have been central in the development of complex analysis in finitely many variables, and constitute one of the most promising lines of research in infinite dimensional complex analysis. This book presents a unified view of these topics in both finite and infinite dimensions.
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Introduction to Complex Analysis in Several Variables

Author: Volker Scheidemann

Publisher: Springer Science & Business Media

ISBN: 9783764374914

Category: Mathematics

Page: 171

View: 999

This book provides a comprehensive introduction to complex analysis in several variables. One major focus of the book is extension phenomena alien to the one-dimensional theory (Hartog's Kugelsatz, theorem of Cartan-Thullen, Bochner's theorem). The book primarily aims at students starting to work in the field of complex analysis in several variables and teachers who want to prepare a university lecture. Therefore, the book contains more than 50 examples and more than 100 supporting exercises.
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Complex Analysis

In the Spirit of Lipman Bers

Author: Jane P. Gilman,Irwin Kra,Rubí E. Rodríguez

Publisher: Springer Science & Business Media

ISBN: 038774715X

Category: Mathematics

Page: 220

View: 1336

The authors’ aim here is to present a precise and concise treatment of those parts of complex analysis that should be familiar to every research mathematician. They follow a path in the tradition of Ahlfors and Bers by dedicating the book to a very precise goal: the statement and proof of the Fundamental Theorem for functions of one complex variable. They discuss the many equivalent ways of understanding the concept of analyticity, and offer a leisure exploration of interesting consequences and applications. Readers should have had undergraduate courses in advanced calculus, linear algebra, and some abstract algebra. No background in complex analysis is required.
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Fundamentals and Applications of Complex Analysis

Author: Harold Cohen

Publisher: Springer Science & Business Media

ISBN: 9780306477485

Category: Mathematics

Page: 418

View: 9559

This book is intended to serve as a text for first and second year courses in single variable complex analysis. The material that is appropriate for more advanced study is developed from elementary material. The concepts are illustrated with large numbers of examples, many of which involve problems students encounter in other courses. For example, students who have taken an introductory physics course will have encountered analysis of simple AC circuits. This text revisits such analysis using complex numbers. Cauchy's residue theorem is used to evaluate many types of definite integrals that students are introduced to in the beginning calculus sequence. Methods of conformal mapping are used to solve problems in electrostatics. The book contains material that is not considered in other popular complex analysis texts.
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Functions of One Complex Variable I

Author: John B. Conway

Publisher: Springer Science & Business Media

ISBN: 9780387903286

Category: Mathematics

Page: 317

View: 5650

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.
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Holomorphic Functions and Integral Representations in Several Complex Variables

Author: R. Michael Range

Publisher: Springer Science & Business Media

ISBN: 1475719183

Category: Mathematics

Page: 392

View: 5809

The subject of this book is Complex Analysis in Several Variables. This text begins at an elementary level with standard local results, followed by a thorough discussion of the various fundamental concepts of "complex convexity" related to the remarkable extension properties of holomorphic functions in more than one variable. It then continues with a comprehensive introduction to integral representations, and concludes with complete proofs of substantial global results on domains of holomorphy and on strictly pseudoconvex domains inC", including, for example, C. Fefferman's famous Mapping Theorem. The most important new feature of this book is the systematic inclusion of many of the developments of the last 20 years which centered around integral representations and estimates for the Cauchy-Riemann equations. In particu lar, integral representations are the principal tool used to develop the global theory, in contrast to many earlier books on the subject which involved methods from commutative algebra and sheaf theory, and/or partial differ ential equations. I believe that this approach offers several advantages: (1) it uses the several variable version of tools familiar to the analyst in one complex variable, and therefore helps to bridge the often perceived gap between com plex analysis in one and in several variables; (2) it leads quite directly to deep global results without introducing a lot of new machinery; and (3) concrete integral representations lend themselves to estimations, therefore opening the door to applications not accessible by the earlier methods.
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Concise Complex Analysis

Author: Sheng Gong,Youhong Gong

Publisher: World Scientific

ISBN: 9812706933

Category: Science

Page: 237

View: 6364

"This is a concise textbook of complex analysis for undergraduate and graduate students. Written from the viewpoint of modern mathematics - the d-equation, differential geometry, Lie group, etc. it contains all the traditional material on complex analysis. However, many statement and proofs of classical theorems in complex analysis have been made simpler, shorter and more elegant due to modern mathematical ideas and methods. For example, the Mittag-Leffer theorem is proved by the d-equation, the Picard theorem is proved using the methods of differential geometry, and so on."--BOOK JACKET.
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Harmonic and Complex Analysis in Several Variables

Author: Steven G. Krantz

Publisher: Springer

ISBN: 3319632310

Category: Mathematics

Page: 424

View: 1950

Authored by a ranking authority in harmonic analysis of several complex variables, this book embodies a state-of-the-art entrée at the intersection of two important fields of research: complex analysis and harmonic analysis. Written with the graduate student in mind, it is assumed that the reader has familiarity with the basics of complex analysis of one and several complex variables as well as with real and functional analysis. The monograph is largely self-contained and develops the harmonic analysis of several complex variables from the first principles. The text includes copious examples, explanations, an exhaustive bibliography for further reading, and figures that illustrate the geometric nature of the subject. Each chapter ends with an exercise set. Additionally, each chapter begins with a prologue, introducing the reader to the subject matter that follows; capsules presented in each section give perspective and a spirited launch to the segment; preludes help put ideas into context. Mathematicians and researchers in several applied disciplines will find the breadth and depth of the treatment of the subject highly useful.
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Complex Variables

An Introduction

Author: Carlos A. Berenstein,Roger Gay

Publisher: Springer Science & Business Media

ISBN: 9780387973494

Category: Mathematics

Page: 650

View: 2288

Textbooks, even excellent ones, are a reflection of their times. Form and content of books depend on what the students know already, what they are expected to learn, how the subject matter is regarded in relation to other divisions of mathematics, and even how fashionable the subject matter is. It is thus not surprising that we no longer use such masterpieces as Hurwitz and Courant's Funktionentheorie or Jordan's Cours d'Analyse in our courses. The last two decades have seen a significant change in the techniques used in the theory of functions of one complex variable. The important role played by the inhomogeneous Cauchy-Riemann equation in the current research has led to the reunification, at least in their spirit, of complex analysis in one and in several variables. We say reunification since we think that Weierstrass, Poincare, and others (in contrast to many of our students) did not consider them to be entirely separate subjects. Indeed, not only complex analysis in several variables, but also number theory, harmonic analysis, and other branches of mathematics, both pure and applied, have required a reconsidera tion of analytic continuation, ordinary differential equations in the complex domain, asymptotic analysis, iteration of holomorphic functions, and many other subjects from the classic theory of functions of one complex variable. This ongoing reconsideration led us to think that a textbook incorporating some of these new perspectives and techniques had to be written.
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