Complex Analysis And Related Topics

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Topics in Complex Analysis

Mats Andersson
Topics in Complex Analysis Book PDF

Author : Mats Andersson
Publisher : Springer Science & Business Media
Page : 166 pages
File Size : 54,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461240426

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Topics in Complex Analysis by Mats Andersson Pdf

This book is an outgrowth of lectures given on several occasions at Chalmers University of Technology and Goteborg University during the last ten years. As opposed to most introductory books on complex analysis, this one as sumes that the reader has previous knowledge of basic real analysis. This makes it possible to follow a rather quick route through the most fundamen tal material on the subject in order to move ahead to reach some classical highlights (such as Fatou theorems and some Nevanlinna theory), as well as some more recent topics (for example, the corona theorem and the HI_ BMO duality) within the time frame of a one-semester course. Sections 3 and 4 in Chapter 2, Sections 5 and 6 in Chapter 3, Section 3 in Chapter 5, and Section 4 in Chapter 7 were not contained in my original lecture notes and therefore might be considered special topics. In addition, they are completely independent and can be omitted with no loss of continuity. The order of the topics in the exposition coincides to a large degree with historical developments. The first five chapters essentially deal with theory developed in the nineteenth century, whereas the remaining chapters contain material from the early twentieth century up to the 1980s. Choosing methods of presentation and proofs is a delicate task. My aim has been to point out connections with real analysis and harmonic anal ysis, while at the same time treating classical complex function theory.

Complex Analysis and Special Topics in Harmonic Analysis

Carlos A. Berenstein,Roger Gay
Complex Analysis and Special Topics in Harmonic Analysis Book PDF

Author : Carlos A. Berenstein,Roger Gay
Publisher : Springer Science & Business Media
Page : 491 pages
File Size : 40,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461384458

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Complex Analysis and Special Topics in Harmonic Analysis by Carlos A. Berenstein,Roger Gay Pdf

A companion volume to the text "Complex Variables: An Introduction" by the same authors, this book further develops the theory, continuing to emphasize the role that the Cauchy-Riemann equation plays in modern complex analysis. Topics considered include: Boundary values of holomorphic functions in the sense of distributions; interpolation problems and ideal theory in algebras of entire functions with growth conditions; exponential polynomials; the G transform and the unifying role it plays in complex analysis and transcendental number theory; summation methods; and the theorem of L. Schwarz concerning the solutions of a homogeneous convolution equation on the real line and its applications in harmonic function theory.

Topics in Complex Analysis

Dorothy Brown Shaffer
Topics in Complex Analysis Book PDF

Author : Dorothy Brown Shaffer
Publisher : American Mathematical Soc.
Page : 141 pages
File Size : 41,8 Mb
Release : 1985
Category : Mathematics
ISBN : 9780821850374

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Topics in Complex Analysis by Dorothy Brown Shaffer Pdf

Most of the mathematical ideas presented in this volume are based on papers given at an AMS meeting held at Fairfield University in October 1983. The unifying theme of the talks was Geometric Function Theory. Papers in this volume generally represent extended versions of the talks presented by the authors. In addition, the proceedings contain several papers that could not be given in person. A few of the papers have been expanded to include further research results obtained in the time between the conference and submission of manuscripts. In most cases, an expository section or history of recent research has been added. The authors' new research results are incorporated into this more general framework. The collection represents a survey of research carried out in recent years in a variety of topics. The paper by Y. J. Leung deals with the Loewner equation, classical results on coefficient bodies and modern optimal control theory.Glenn Schober writes about the class $\Sigma$, its support points and extremal configurations. Peter Duren deals with support points for the class $S$, Loewner chains and the process of truncation. A very complete survey about the role of polynomials and their limits in class $S$ is contributed by T. J. Suffridge. A generalization of the univalence criterion due to Nehari and its relation to the hyperbolic metric is contained in the paper by David Minda. The omitted area problem for functions in class $S$ is solved in the paper by Roger Barnard. New results on angular derivatives and domains are represented in the paper by Burton Rodin and Stefan E. Warschawski, while estimates on the radial growth of the derivative of univalent functions are given by Thom MacGregor. In the paper by B. Bshouty and W. Hengartner a conjecture of Bombieri is proved for some cases.Other interesting problems for special subclasses are solved by B. A. Case and J. R. Quine; M. O. Reade, H. Silverman and P. G. Todorov; and, H. Silverman and E. M. Silvia. New univalence criteria for integral transforms are given by Edward Merkes. Potential theoretic results are represented in the paper by Jack Quine with new results on the Star Function and by David Tepper with free boundary problems in the flow around an obstacle. Approximation by functions which are the solutions of more general elliptic equations are treated by A. Dufresnoy, P. M. Gauthier and W. H. Ow. At the time of preparation of these manuscripts, nothing was known about the proof of the Bieberbach conjecture. Many of the authors of this volume and other experts in the field were recently interviewed by the editor regarding the effect of the proof of the conjecture. Their ideas regarding future trends in research in complex analysis are presented in the epilogue by Dorothy Shaffer.A graduate level course in complex analysis provides adequate background for the enjoyment of this book.

Visual Complex Analysis

Tristan Needham
Visual Complex Analysis Book PDF

Author : Tristan Needham
Publisher : Oxford University Press
Page : 620 pages
File Size : 40,7 Mb
Release : 1997
Category : Mathematics
ISBN : 0198534469

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Visual Complex Analysis by Tristan Needham Pdf

This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.

Elementary Real and Complex Analysis

Georgi E. Shilov,Georgij Evgen'evi? Šilov,Richard A. Silverman
Elementary Real and Complex Analysis Book PDF

Author : Georgi E. Shilov,Georgij Evgen'evi? Šilov,Richard A. Silverman
Publisher : Courier Corporation
Page : 548 pages
File Size : 51,8 Mb
Release : 1996-01-01
Category : Mathematics
ISBN : 0486689220

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Elementary Real and Complex Analysis by Georgi E. Shilov,Georgij Evgen'evi? Šilov,Richard A. Silverman Pdf

Excellent undergraduate-level text offers coverage of real numbers, sets, metric spaces, limits, continuous functions, much more. Each chapter contains a problem set with hints and answers. 1973 edition.

A Collection of Problems on Complex Analysis

Lev Izrailevich Volkovyski?,Grigori? L?vovich Lunt?s?,Isaak Genrikhovich Aramanovich,J. Berry,T. Kovari
A Collection of Problems on Complex Analysis Book PDF

Author : Lev Izrailevich Volkovyski?,Grigori? L?vovich Lunt?s?,Isaak Genrikhovich Aramanovich,J. Berry,T. Kovari
Publisher : Courier Corporation
Page : 450 pages
File Size : 53,6 Mb
Release : 1991-01-01
Category : Mathematics
ISBN : 9780486669137

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A Collection of Problems on Complex Analysis by Lev Izrailevich Volkovyski?,Grigori? L?vovich Lunt?s?,Isaak Genrikhovich Aramanovich,J. Berry,T. Kovari Pdf

Over 1500 problems on theory of functions of the complex variable; coverage of nearly every branch of classical function theory. Topics include conformal mappings, integrals and power series, Laurent series, parametric integrals, integrals of the Cauchy type, analytic continuation, Riemann surfaces, much more. Answers and solutions at end of text. Bibliographical references. 1965 edition.

Complex Analysis

Elias M. Stein,Rami Shakarchi
Complex Analysis Book PDF

Author : Elias M. Stein,Rami Shakarchi
Publisher : Princeton University Press
Page : 398 pages
File Size : 55,8 Mb
Release : 2010-04-22
Category : Mathematics
ISBN : 9781400831159

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Complex Analysis by Elias M. Stein,Rami Shakarchi Pdf

With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle. With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory. Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, Complex Analysis will be welcomed by students of mathematics, physics, engineering and other sciences. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Complex Analysis is the second, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.

Principles of Complex Analysis

Serge Lvovski
Principles of Complex Analysis Book PDF

Author : Serge Lvovski
Publisher : Springer Nature
Page : 257 pages
File Size : 53,7 Mb
Release : 2020-09-26
Category : Mathematics
ISBN : 9783030593650

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Principles of Complex Analysis by Serge Lvovski Pdf

This is a brief textbook on complex analysis intended for the students of upper undergraduate or beginning graduate level. The author stresses the aspects of complex analysis that are most important for the student planning to study algebraic geometry and related topics. The exposition is rigorous but elementary: abstract notions are introduced only if they are really indispensable. This approach provides a motivation for the reader to digest more abstract definitions (e.g., those of sheaves or line bundles, which are not mentioned in the book) when he/she is ready for that level of abstraction indeed. In the chapter on Riemann surfaces, several key results on compact Riemann surfaces are stated and proved in the first nontrivial case, i.e. that of elliptic curves.

Current Topics in Pure and Computational Complex Analysis

Santosh Joshi,Michael Dorff,Indrajit Lahiri
Current Topics in Pure and Computational Complex Analysis Book PDF

Author : Santosh Joshi,Michael Dorff,Indrajit Lahiri
Publisher : Springer
Page : 258 pages
File Size : 47,5 Mb
Release : 2014-12-02
Category : Mathematics
ISBN : 9788132221135

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Current Topics in Pure and Computational Complex Analysis by Santosh Joshi,Michael Dorff,Indrajit Lahiri Pdf

The book contains 13 articles, some of which are survey articles and others research papers. Written by eminent mathematicians, these articles were presented at the International Workshop on Complex Analysis and Its Applications held at Walchand College of Engineering, Sangli. All the contributing authors are actively engaged in research fields related to the topic of the book. The workshop offered a comprehensive exposition of the recent developments in geometric functions theory, planar harmonic mappings, entire and meromorphic functions and their applications, both theoretical and computational. The recent developments in complex analysis and its applications play a crucial role in research in many disciplines.

Complex Analysis

Mario Gonzalez
Complex Analysis Book PDF

Author : Mario Gonzalez
Publisher : Routledge
Page : 250 pages
File Size : 51,7 Mb
Release : 2018-03-09
Category : Mathematics
ISBN : 9781351459372

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Complex Analysis by Mario Gonzalez Pdf

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

Geometric Analysis of Several Complex Variables and Related Topics

Y. Barkatou
Geometric Analysis of Several Complex Variables and Related Topics Book PDF

Author : Y. Barkatou
Publisher : American Mathematical Soc.
Page : 208 pages
File Size : 47,5 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821852576

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Geometric Analysis of Several Complex Variables and Related Topics by Y. Barkatou Pdf

Presents current research and future trends in the theory of several complex variables and PDE. Of note are two survey articles, the first presenting recent results on the solvability of complex vector fields with critical points, while the second concerns the Lie group structure of the automorphism groups of CR manifolds.

Complex Analysis

Serge Lang
Complex Analysis Book PDF

Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 380 pages
File Size : 41,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475718713

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Complex Analysis by Serge Lang Pdf

The present book is meant as a text for a course on complex analysis at the advanced undergraduate level, or first-year graduate level. Somewhat more material has been included than can be covered at leisure in one term, to give opportunities for the instructor to exercise his taste, and lead the course in whatever direction strikes his fancy at the time. A large number of routine exercises are included for the more standard portions, and a few harder exercises of striking theoretical interest are also included, but may be omitted in courses addressed to less advanced students. In some sense, I think the classical German prewar texts were the best (Hurwitz-Courant, Knopp, Bieberbach, etc. ) and I would recom mend to anyone to look through them. More recent texts have empha sized connections with real analysis, which is important, but at the cost of exhibiting succinctly and clearly what is peculiar about complex anal ysis: the power series expansion, the uniqueness of analytic continuation, and the calculus of residues. The systematic elementary development of formal and convergent power series was standard fare in the German texts, but only Cartan, in the more recent books, includes this material, which I think is quite essential, e. g. , for differential equations. I have written a short text, exhibiting these features, making it applicable to a wide variety of tastes. The book essentially decomposes into two parts.

Complex Analysis, Operators, and Related Topics

Victor P. Havin,Nikolai K. Nikolski
Complex Analysis Operators and Related Topics Book PDF

Author : Victor P. Havin,Nikolai K. Nikolski
Publisher : Birkhäuser
Page : 407 pages
File Size : 46,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034883788

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Complex Analysis, Operators, and Related Topics by Victor P. Havin,Nikolai K. Nikolski Pdf

This volume is devoted to some topical problems and various applications of operator theory and its interplay with modern complex analysis. 30 carefully selected surveys and research papers are united by the "operator theoretic ideology" and systematic use of modern function theoretical techniques.

A Complex Analysis Problem Book

Daniel Alpay
A Complex Analysis Problem Book Book PDF

Author : Daniel Alpay
Publisher : Birkhäuser
Page : 592 pages
File Size : 47,6 Mb
Release : 2016-10-26
Category : Mathematics
ISBN : 9783319421810

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A Complex Analysis Problem Book by Daniel Alpay Pdf

This second edition presents a collection of exercises on the theory of analytic functions, including completed and detailed solutions. It introduces students to various applications and aspects of the theory of analytic functions not always touched on in a first course, while also addressing topics of interest to electrical engineering students (e.g., the realization of rational functions and its connections to the theory of linear systems and state space representations of such systems). It provides examples of important Hilbert spaces of analytic functions (in particular the Hardy space and the Fock space), and also includes a section reviewing essential aspects of topology, functional analysis and Lebesgue integration. Benefits of the 2nd edition Rational functions are now covered in a separate chapter. Further, the section on conformal mappings has been expanded.

Modern Real and Complex Analysis

Bernard R. Gelbaum
Modern Real and Complex Analysis Book PDF

Author : Bernard R. Gelbaum
Publisher : John Wiley & Sons
Page : 506 pages
File Size : 49,8 Mb
Release : 2011-02-25
Category : Mathematics
ISBN : 9781118030806

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Modern Real and Complex Analysis by Bernard R. Gelbaum Pdf

Modern Real and Complex Analysis Thorough, well-written, and encyclopedic in its coverage, this textoffers a lucid presentation of all the topics essential to graduatestudy in analysis. While maintaining the strictest standards ofrigor, Professor Gelbaum's approach is designed to appeal tointuition whenever possible. Modern Real and Complex Analysisprovides up-to-date treatment of such subjects as the Daniellintegration, differentiation, functional analysis and Banachalgebras, conformal mapping and Bergman's kernels, defectivefunctions, Riemann surfaces and uniformization, and the role ofconvexity in analysis. The text supplies an abundance of exercisesand illustrative examples to reinforce learning, and extensivenotes and remarks to help clarify important points.