An Advanced Complex Analysis Problem Book
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| Author | : Daniel Alpay |
| Publisher | : Birkhäuser |
| Total Pages | : 592 |
| Release | : 2016-10-26 |
| Genre | : Mathematics |
| ISBN | : 3319421816 |
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.
| Author | : Daniel Alpay |
| Publisher | : Birkhäuser |
| Total Pages | : 523 |
| Release | : 2015-11-13 |
| Genre | : Mathematics |
| ISBN | : 3319160591 |
This is an exercises book at the beginning graduate level, whose aim is to illustrate some of the connections between functional analysis and the theory of functions of one variable. A key role is played by the notions of positive definite kernel and of reproducing kernel Hilbert space. A number of facts from functional analysis and topological vector spaces are surveyed. Then, various Hilbert spaces of analytic functions are studied.
| Author | : Barry Simon |
| Publisher | : |
| Total Pages | : 749 |
| Release | : 2015 |
| Genre | : Mathematical analysis |
| ISBN | : 9781470411039 |
A Comprehensive Course in Analysis by Poincar Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis
| Author | : Lev Izrailevich Volkovyski? |
| Publisher | : Courier Corporation |
| Total Pages | : 450 |
| Release | : 1991-01-01 |
| Genre | : Mathematics |
| ISBN | : 0486669130 |
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.
| Author | : Friedrich Haslinger |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 348 |
| Release | : 2017-11-20 |
| Genre | : Mathematics |
| ISBN | : 3110417243 |
In this textbook, a concise approach to complex analysis of one and several variables is presented. After an introduction of Cauchy‘s integral theorem general versions of Runge‘s approximation theorem and Mittag-Leffler‘s theorem are discussed. The fi rst part ends with an analytic characterization of simply connected domains. The second part is concerned with functional analytic methods: Fréchet and Hilbert spaces of holomorphic functions, the Bergman kernel, and unbounded operators on Hilbert spaces to tackle the theory of several variables, in particular the inhomogeneous Cauchy-Riemann equations and the d-bar Neumann operator. Contents Complex numbers and functions Cauchy’s Theorem and Cauchy’s formula Analytic continuation Construction and approximation of holomorphic functions Harmonic functions Several complex variables Bergman spaces The canonical solution operator to Nuclear Fréchet spaces of holomorphic functions The -complex The twisted -complex and Schrödinger operators
| Author | : Wolfgang Fischer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 280 |
| Release | : 2011-10-21 |
| Genre | : Mathematics |
| ISBN | : 3834886610 |
This carefully written textbook is an introduction to the beautiful concepts and results of complex analysis. It is intended for international bachelor and master programmes in Germany and throughout Europe; in the Anglo-American system of university education the content corresponds to a beginning graduate course. The book presents the fundamental results and methods of complex analysis and applies them to a study of elementary and non-elementary functions (elliptic functions, Gamma- and Zeta function including a proof of the prime number theorem ...) and – a new feature in this context! – to exhibiting basic facts in the theory of several complex variables. Part of the book is a translation of the authors’ German text “Einführung in die komplexe Analysis”; some material was added from the by now almost “classical” text “Funktionentheorie” written by the authors, and a few paragraphs were newly written for special use in a master’s programme.
| Author | : Ravi P. Agarwal |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 345 |
| Release | : 2011-07-01 |
| Genre | : Mathematics |
| ISBN | : 146140195X |
This textbook introduces the subject of complex analysis to advanced undergraduate and graduate students in a clear and concise manner. Key features of this textbook: effectively organizes the subject into easily manageable sections in the form of 50 class-tested lectures, uses detailed examples to drive the presentation, includes numerous exercise sets that encourage pursuing extensions of the material, each with an “Answers or Hints” section, covers an array of advanced topics which allow for flexibility in developing the subject beyond the basics, provides a concise history of complex numbers. An Introduction to Complex Analysis will be valuable to students in mathematics, engineering and other applied sciences. Prerequisites include a course in calculus.
| Author | : Bernard R. Gelbaum |
| Publisher | : John Wiley & Sons |
| Total Pages | : 506 |
| Release | : 2011-02-25 |
| Genre | : Mathematics |
| ISBN | : 111803080X |
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.
| Author | : Steven G. Krantz |
| Publisher | : CRC Press |
| Total Pages | : 322 |
| Release | : 1992-07-02 |
| Genre | : Mathematics |
| ISBN | : 9780849371554 |
Ever since the groundbreaking work of J.J. Kohn in the early 1960s, there has been a significant interaction between the theory of partial differential equations and the function theory of several complex variables. Partial Differential Equations and Complex Analysis explores the background and plumbs the depths of this symbiosis. The book is an excellent introduction to a variety of topics and presents many of the basic elements of linear partial differential equations in the context of how they are applied to the study of complex analysis. The author treats the Dirichlet and Neumann problems for elliptic equations and the related Schauder regularity theory, and examines how those results apply to the boundary regularity of biholomorphic mappings. He studies the ?-Neumann problem, then considers applications to the complex function theory of several variables and to the Bergman projection.
| Author | : Saeed Zakeri |
| Publisher | : Princeton University Press |
| Total Pages | : 442 |
| Release | : 2021-11-02 |
| Genre | : Mathematics |
| ISBN | : 0691207585 |
"This textbook is intended for a year-long graduate course on complex analysis, a branch of mathematical analysis that has broad applications, particularly in physics, engineering, and applied mathematics. Based on nearly twenty years of classroom lectures, the book is accessible enough for independent study, while the rigorous approach will appeal to more experienced readers and scholars, propelling further research in this field. While other graduate-level complex analysis textbooks do exist, Zakeri takes a distinctive approach by highlighting the geometric properties and topological underpinnings of this area. Zakeri includes more than three hundred and fifty problems, with problem sets at the end of each chapter, along with additional solved examples. Background knowledge of undergraduate analysis and topology is needed, but the thoughtful examples are accessible to beginning graduate students and advanced undergraduates. At the same time, the book has sufficient depth for advanced readers to enhance their own research. The textbook is well-written, clearly illustrated, and peppered with historical information, making it approachable without sacrificing rigor. It is poised to be a valuable textbook for graduate students, filling a needed gap by way of its level and unique approach"--
