Differential Calculus and Holomorphy PDF Download

Author: J.F. Colombeau
Publisher: Elsevier
ISBN: 9780080871752
Category : Mathematics
Languages : en
Pages : 454

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Differential Calculus and Holomorphy

Author: Soo Bong Chae
Publisher: CRC Press
ISBN: 1000146537
Category : Mathematics
Languages : en
Pages : 442

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Book Description
This book presents a systematic introduction to the theory of holomorphic mappings in normed spaces which has been scattered throughout the literature. It gives the necessary, elementary background for all branches of modern mathematics involving differential calculus in higher dimensional spaces.

Author: R. Michael Range
Publisher: Springer Science & Business Media
ISBN: 1475719183
Category : Mathematics
Languages : en
Pages : 405

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Book Description
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.

Author: Dmitry Khavinson
Publisher: American Mathematical Soc.
ISBN: 1470437805
Category : Differential equations, Linear
Languages : en
Pages : 214

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Book Description
Why do solutions of linear analytic PDE suddenly break down? What is the source of these mysterious singularities, and how do they propagate? Is there a mean value property for harmonic functions in ellipsoids similar to that for balls? Is there a reflection principle for harmonic functions in higher dimensions similar to the Schwarz reflection principle in the plane? How far outside of their natural domains can solutions of the Dirichlet problem be extended? Where do the continued solutions become singular and why? This book invites graduate students and young analysts to explore these and many other intriguing questions that lead to beautiful results illustrating a nice interplay between parts of modern analysis and themes in “physical” mathematics of the nineteenth century. To make the book accessible to a wide audience including students, the authors do not assume expertise in the theory of holomorphic PDE, and most of the book is accessible to anyone familiar with multivariable calculus and some basics in complex analysis and differential equations.

Author: Guido I. Zapata
Publisher: CRC Press
ISBN: 1000154122
Category : Mathematics
Languages : en
Pages : 476

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Book Description
This book contains papers on complex analysis, function spaces, harmonic analysis, and operators, presented at the International seminar on Functional Analysis, Holomorphy, and Approximation Theory held in 1979. It is addressed to mathematicians and advanced graduate students in mathematics.

Author: L. A. Aizenberg
Publisher: American Mathematical Soc.
ISBN: 082181348X
Category : Mathematics
Languages : en
Pages : 165

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Book Description
The authors consider the problem of characterizing the exterior differential forms which are orthogonal to holomorphic functions (or forms) in a domain $D\subset {\mathbf C}^n$ with respect to integration over the boundary, and some related questions. They give a detailed account of the derivation of the Bochner-Martinelli-Koppelman integral representation of exterior differential forms, which was obtained in 1967 and has already found many important applications. They study the properties of $\overline \partial$-closed forms of type $(p, n - 1), 0\leq p\leq n - 1$, which turn out to be the duals (with respect to the orthogonality mentioned above) to holomorphic functions (or forms) in several complex variables, and resemble holomorphic functions of one complex variable in their properties.

Author: Elias M. Stein
Publisher: Princeton University Press
ISBN: 1400871263
Category : Mathematics
Languages : en
Pages : 83

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Book Description
This book has as its subject the boundary value theory of holomorphic functions in several complex variables, a topic that is just now coming to the forefront of mathematical analysis. For one variable, the topic is classical and rather well understood. In several variables, the necessary understanding of holomorphic functions via partial differential equations has a recent origin, and Professor Stein's book, which emphasizes the potential-theoretic aspects of the boundary value problem, should become the standard work in the field. Originally published in 1972. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Author: Jorge Mujica
Publisher: Courier Corporation
ISBN: 0486474666
Category : Mathematics
Languages : en
Pages : 466

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Book Description
The development of complex analysis is based on issues related to holomorphic continuation and holomorphic approximation. This volume presents a unified view of these topics in finite and infinite dimensions. A high-level tutorial in pure and applied mathematics, its prerequisites include a familiarity with the basic properties of holomorphic functions, the principles of Banach and Hilbert spaces, and the theory of Lebesgue integration. The four-part treatment begins with an overview of the basic properties of holomorphic mappings and holomorphic domains in Banach spaces. The second section explores differentiable mappings, differentiable forms, and polynomially convex compact sets, in which the results are applied to the study of Banach and Fréchet algebras. Subsequent sections examine plurisubharmonic functions and pseudoconvex domains in Banach spaces, along with Riemann domains and envelopes of holomorphy. In addition to its value as a text for advanced graduate students of mathematics, this volume also functions as a reference for researchers and professionals.

Author: S. B. Chae
Publisher: CRC Press
ISBN: 9780824772314
Category : Mathematics
Languages : en
Pages : 444

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Book Description
This book presents a systematic introduction to the theory of holomorphic mappings in normed spaces which has been scattered throughout the literature. It gives the necessary, elementary background for all branches of modern mathematics involving differential calculus in higher dimensional spaces.

Author: Luis Barreira
Publisher: Springer Science & Business Media
ISBN: 1447140087
Category : Mathematics
Languages : en
Pages : 417

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Book Description
This text provides an accessible, self-contained and rigorous introduction to complex analysis and differential equations. Topics covered include holomorphic functions, Fourier series, ordinary and partial differential equations. The text is divided into two parts: part one focuses on complex analysis and part two on differential equations. Each part can be read independently, so in essence this text offers two books in one. In the second part of the book, some emphasis is given to the application of complex analysis to differential equations. Half of the book consists of approximately 200 worked out problems, carefully prepared for each part of theory, plus 200 exercises of variable levels of difficulty. Tailored to any course giving the first introduction to complex analysis or differential equations, this text assumes only a basic knowledge of linear algebra and differential and integral calculus. Moreover, the large number of examples, worked out problems and exercises makes this the ideal book for independent study.