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Schwarz Lemma For Analytic Functions Of Two Complex Variables
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Book Synopsis Complex Analysis by : Theodore W. Gamelin
Download or read book Complex Analysis written by Theodore W. Gamelin and published by Springer Science & Business Media. This book was released on 2013-11-01 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to complex analysis for students with some knowledge of complex numbers from high school. It contains sixteen chapters, the first eleven of which are aimed at an upper division undergraduate audience. The remaining five chapters are designed to complete the coverage of all background necessary for passing PhD qualifying exams in complex analysis. Topics studied include Julia sets and the Mandelbrot set, Dirichlet series and the prime number theorem, and the uniformization theorem for Riemann surfaces, with emphasis placed on the three geometries: spherical, euclidean, and hyperbolic. Throughout, exercises range from the very simple to the challenging. The book is based on lectures given by the author at several universities, including UCLA, Brown University, La Plata, Buenos Aires, and the Universidad Autonomo de Valencia, Spain.
Download or read book The Schwarz Lemma written by Sean Dineen and published by Courier Dover Publications. This book was released on 2016-04-06 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for advanced undergraduates and graduate students, this self-contained overview covers the classical Schwarz lemma, Poincaré distance on the unit disc, hyperbolic manifolds, holomorphic curvature, and the analytic Radon-Nikodym property. 1989 edition.
Book Synopsis Complex Analysis by : Elias M. Stein
Download or read book Complex Analysis written by Elias M. Stein and published by Princeton University Press. This book was released on 2010-04-22 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Entire Functions of Several Complex Variables by : Pierre Lelong
Download or read book Entire Functions of Several Complex Variables written by Pierre Lelong and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: I - Entire functions of several complex variables constitute an important and original chapter in complex analysis. The study is often motivated by certain applications to specific problems in other areas of mathematics: partial differential equations via the Fourier-Laplace transformation and convolution operators, analytic number theory and problems of transcen dence, or approximation theory, just to name a few. What is important for these applications is to find solutions which satisfy certain growth conditions. The specific problem defines inherently a growth scale, and one seeks a solution of the problem which satisfies certain growth conditions on this scale, and sometimes solutions of minimal asymp totic growth or optimal solutions in some sense. For one complex variable the study of solutions with growth conditions forms the core of the classical theory of entire functions and, historically, the relationship between the number of zeros of an entire function f(z) of one complex variable and the growth of If I (or equivalently log If I) was the first example of a systematic study of growth conditions in a general setting. Problems with growth conditions on the solutions demand much more precise information than existence theorems. The correspondence between two scales of growth can be interpreted often as a correspondence between families of bounded sets in certain Frechet spaces. However, for applications it is of utmost importance to develop precise and explicit representations of the solutions.
Book Synopsis Tasty Bits of Several Complex Variables by : Jiri Lebl
Download or read book Tasty Bits of Several Complex Variables written by Jiri Lebl and published by Lulu.com. This book was released on 2016-05-05 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a polished version of my course notes for Math 6283, Several Complex Variables, given in Spring 2014 and Spring 2016 semester at Oklahoma State University. The course covers basics of holomorphic function theory, CR geometry, the dbar problem, integral kernels and basic theory of complex analytic subvarieties. See http: //www.jirka.org/scv/ for more information.
Book Synopsis Elementary Theory of Analytic Functions of One or Several Complex Variables by : Henri Cartan
Download or read book Elementary Theory of Analytic Functions of One or Several Complex Variables written by Henri Cartan and published by Courier Corporation. This book was released on 2013-04-22 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Pick Interpolation and Hilbert Function Spaces by : Jim Agler
Download or read book Pick Interpolation and Hilbert Function Spaces written by Jim Agler and published by American Mathematical Society. This book was released on 2023-02-22 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book first rigorously develops the theory of reproducing kernel Hilbert spaces. The authors then discuss the Pick problem of finding the function of smallest $H^infty$ norm that has specified values at a finite number of points in the disk. Their viewpoint is to consider $H^infty$ as the multiplier algebra of the Hardy space and to use Hilbert space techniques to solve the problem. This approach generalizes to a wide collection of spaces. The authors then consider the interpolation problem in the space of bounded analytic functions on the bidisk and give a complete description of the solution. They then consider very general interpolation problems. The book includes developments of all the theory that is needed, including operator model theory, the Arveson extension theorem, and the hereditary functional calculus.
Book Synopsis Complex Analysis through Examples and Exercises by : E. Pap
Download or read book Complex Analysis through Examples and Exercises written by E. Pap and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book Complex Analysis through Examples and Exercises has come out from the lectures and exercises that the author held mostly for mathematician and physists . The book is an attempt to present the rat her involved subject of complex analysis through an active approach by the reader. Thus this book is a complex combination of theory and examples. Complex analysis is involved in all branches of mathematics. It often happens that the complex analysis is the shortest path for solving a problem in real circum stances. We are using the (Cauchy) integral approach and the (Weierstrass) power se ries approach . In the theory of complex analysis, on the hand one has an interplay of several mathematical disciplines, while on the other various methods, tools, and approaches. In view of that, the exposition of new notions and methods in our book is taken step by step. A minimal amount of expository theory is included at the beinning of each section, the Preliminaries, with maximum effort placed on weil selected examples and exercises capturing the essence of the material. Actually, I have divided the problems into two classes called Examples and Exercises (some of them often also contain proofs of the statements from the Preliminaries). The examples contain complete solutions and serve as a model for solving similar problems given in the exercises. The readers are left to find the solution in the exercisesj the answers, and, occasionally, some hints, are still given.
Book Synopsis Complex Variables by : Robert B. Ash
Download or read book Complex Variables written by Robert B. Ash and published by Courier Corporation. This book was released on 2007-01-01 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text on complex variables is geared toward graduate students and undergraduates who have taken an introductory course in real analysis. It is a substantially revised and updated edition of the popular text by Robert B. Ash, offering a concise treatment that provides careful and complete explanations as well as numerous problems and solutions. An introduction presents basic definitions, covering topology of the plane, analytic functions, real-differentiability and the Cauchy-Riemann equations, and exponential and harmonic functions. Succeeding chapters examine the elementary theory and the general Cauchy theorem and its applications, including singularities, residue theory, the open mapping theorem for analytic functions, linear fractional transformations, conformal mapping, and analytic mappings of one disk to another. The Riemann mapping theorem receives a thorough treatment, along with factorization of analytic functions. As an application of many of the ideas and results appearing in earlier chapters, the text ends with a proof of the prime number theorem.
Book Synopsis Visual Complex Analysis by : Tristan Needham
Download or read book Visual Complex Analysis written by Tristan Needham and published by Oxford University Press. This book was released on 1997 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Constantin Carathéodory by : Maria Georgiadou
Download or read book Constantin Carathéodory written by Maria Georgiadou and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 667 pages. Available in PDF, EPUB and Kindle. Book excerpt: With breathtaking detail, Maria Georgiadou sheds light on the work and life of Constantin Carathéodory, who until now has been ignored by historians. In her thought-provoking book, Georgiadou maps out the mathematician’s oeuvre, life and turbulent historical surroundings. Descending from the Greek élite of Constantinople, Carathéodory graduated from the military school of Brussels, became engineer at the Assiout dam in Egypt and finally dedicated a lifetime to mathematics and education. He significantly contributed to: calculus of variations, the theory of point set measure, the theory of functions of a real variable, pdes, and complex function theory. An exciting and well-written biography, once started, difficult to put down.
Download or read book Complex Analysis written by Joseph Bak and published by Springer Science & Business Media. This book was released on 2010-08-02 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unusual and lively textbook offers a clear and intuitive approach to the classical and beautiful theory of complex variables. With very little dependence on advanced concepts from several-variable calculus and topology, the text focuses on the authentic complex-variable ideas and techniques. Accessible to students at their early stages of mathematical study, this full first year course in complex analysis offers new and interesting motivations for classical results and introduces related topics stressing motivation and technique. Numerous illustrations, examples, and now 300 exercises, enrich the text. Students who master this textbook will emerge with an excellent grounding in complex analysis, and a solid understanding of its wide applicability.
Book Synopsis A Guide to Complex Variables by : Steven G. Krantz
Download or read book A Guide to Complex Variables written by Steven G. Krantz and published by American Mathematical Soc.. This book was released on 2014-05-14 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: A quick and easy-to-use introduction to the key topics in complex variables, for mathematicians and non-mathematicians alike.
Book Synopsis Functions of One Complex Variable II by : John B. Conway
Download or read book Functions of One Complex Variable II written by John B. Conway and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Guide to Cultivating Complex Analysis by : Jiri Lebl
Download or read book Guide to Cultivating Complex Analysis written by Jiri Lebl and published by . This book was released on 2020-09-16 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory course in complex analysis for incoming graduate students. Created to teach Math 5283 at Oklahoma State University. The book has somewhat more material than could fit in a one-semester course, allowing some choices. There are also appendices on metric spaces and some basic analysis background to make for a longer and more complete course for those that have only had an introduction to basic analysis on the real line.
Book Synopsis Complex Function Theory by : Donald Sarason
Download or read book Complex Function Theory written by Donald Sarason and published by American Mathematical Society. This book was released on 2021-02-16 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex Function Theory is a concise and rigorous introduction to the theory of functions of a complex variable. Written in a classical style, it is in the spirit of the books by Ahlfors and by Saks and Zygmund. Being designed for a one-semester course, it is much shorter than many of the standard texts. Sarason covers the basic material through Cauchy's theorem and applications, plus the Riemann mapping theorem. It is suitable for either an introductory graduate course or an undergraduate course for students with adequate preparation. The first edition was published with the title Notes on Complex Function Theory.
Book Synopsis Classical Analysis in the Complex Plane by : Robert B. Burckel
Download or read book Classical Analysis in the Complex Plane written by Robert B. Burckel and published by Springer Nature. This book was released on 2021-10-11 with total page 1123 pages. Available in PDF, EPUB and Kindle. Book excerpt: This authoritative text presents the classical theory of functions of a single complex variable in complete mathematical and historical detail. Requiring only minimal, undergraduate-level prerequisites, it covers the fundamental areas of the subject with depth, precision, and rigor. Standard and novel proofs are explored in unusual detail, and exercises – many with helpful hints – provide ample opportunities for practice and a deeper understanding of the material. In addition to the mathematical theory, the author also explores how key ideas in complex analysis have evolved over many centuries, allowing readers to acquire an extensive view of the subject’s development. Historical notes are incorporated throughout, and a bibliography containing more than 2,000 entries provides an exhaustive list of both important and overlooked works. Classical Analysis in the Complex Plane will be a definitive reference for both graduate students and experienced mathematicians alike, as well as an exemplary resource for anyone doing scholarly work in complex analysis. The author’s expansive knowledge of and passion for the material is evident on every page, as is his desire to impart a lasting appreciation for the subject. “I can honestly say that Robert Burckel’s book has profoundly influenced my view of the subject of complex analysis. It has given me a sense of the historical flow of ideas, and has acquainted me with byways and ancillary results that I never would have encountered in the ordinary course of my work. The care exercised in each of his proofs is a model of clarity in mathematical writing...Anyone in the field should have this book on [their bookshelves] as a resource and an inspiration.”- From the Foreword by Steven G. Krantz
