[PDF] A Complex Analysis Problem Book eBook

Author : Daniel Alpay
Publisher : Birkhäuser
Page : 592 pages
File Size : 26,38 MB
Release : 2016-10-26
Category : Mathematics
ISBN : 3319421816

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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 : Lev Izrailevich Volkovyski?
Publisher : Courier Corporation
Page : 450 pages
File Size : 32,4 MB
Release : 1991-01-01
Category : Mathematics
ISBN : 0486669130

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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 : Bernard R. Gelbaum
Publisher : John Wiley & Sons
Page : 506 pages
File Size : 30,88 MB
Release : 2011-02-25
Category : Mathematics
ISBN : 111803080X

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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 : Daniel Alpay
Publisher : Birkhäuser
Page : 523 pages
File Size : 42,84 MB
Release : 2015-11-13
Category : Mathematics
ISBN : 3319160591

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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 : Bernard R. Gelbaum
Publisher : Springer Science & Business Media
Page : 490 pages
File Size : 14,88 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461209250

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This text covers many principal topics in the theory of functions of a complex variable. These include, in real analysis, set algebra, measure and topology, real- and complex-valued functions, and topological vector spaces. In complex analysis, they include polynomials and power series, functions holomorphic in a region, entire functions, analytic continuation, singularities, harmonic functions, families of functions, and convexity theorems.

Author : Friedrich Haslinger
Publisher : Walter de Gruyter GmbH & Co KG
Page : 348 pages
File Size : 15,84 MB
Release : 2017-11-20
Category : Mathematics
ISBN : 3110417243

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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 : Theodore W. Gamelin
Publisher : Springer Science & Business Media
Page : 508 pages
File Size : 50,35 MB
Release : 2013-11-01
Category : Mathematics
ISBN : 0387216073

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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.

Author : David C. Ullrich
Publisher : American Mathematical Soc.
Page : 506 pages
File Size : 36,58 MB
Release : 2008
Category : Mathematics
ISBN : 0821844792

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Presents the Dirichlet problem for harmonic functions twice: once using the Poisson integral for the unit disk and again in an informal section on Brownian motion, where the reader can understand intuitively how the Dirichlet problem works for general domains. This book is suitable for a first-year course in complex analysis

Author : Richard A. Silverman
Publisher : Courier Corporation
Page : 402 pages
File Size : 30,87 MB
Release : 2013-04-15
Category : Mathematics
ISBN : 0486318524

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Shorter version of Markushevich's Theory of Functions of a Complex Variable, appropriate for advanced undergraduate and graduate courses in complex analysis. More than 300 problems, some with hints and answers. 1967 edition.

Author : Henri Cartan
Publisher : Courier Corporation
Page : 242 pages
File Size : 21,81 MB
Release : 2013-04-22
Category : Mathematics
ISBN : 0486318672

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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.