Download or read book Differential Calculus and Holomorphy written by J.F. Colombeau and published by Elsevier. This book was released on 2011-08-18 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Calculus and Holomorphy
Download or read book Holomorphy and Calculus in Normed SPates written by Soo Bong Chae and published by CRC Press. This book was released on 2020-11-26 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Differential Calculus and Holomorphy written by Jean François Colombeau and published by . This book was released on 1982 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Linear Holomorphic Partial Differential Equations and Classical Potential Theory written by Dmitry Khavinson and published by American Mathematical Soc.. This book was released on 2018-07-09 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Complex Analysis and Differential Equations written by Luis Barreira and published by Springer Science & Business Media. This book was released on 2012-04-23 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Holomorphic Functions in the Plane and n dimensional Space written by Klaus Gürlebeck and published by Springer Science & Business Media. This book was released on 2007-11-16 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex analysis nowadays has higher-dimensional analoga: the algebra of complex numbers is replaced then by the non-commutative algebra of real quaternions or by Clifford algebras. During the last 30 years the so-called quaternionic and Clifford or hypercomplex analysis successfully developed to a powerful theory with many applications in analysis, engineering and mathematical physics. This textbook introduces both to classical and higher-dimensional results based on a uniform notion of holomorphy. Historical remarks, lots of examples, figures and exercises accompany each chapter.
Download or read book Analysis II written by Roger Godement and published by Springer Science & Business Media. This book was released on 2006-09-11 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functions in R and C, including the theory of Fourier series, Fourier integrals and part of that of holomorphic functions, form the focal topic of these two volumes. Based on a course given by the author to large audiences at Paris VII University for many years, the exposition proceeds somewhat nonlinearly, blending rigorous mathematics skilfully with didactical and historical considerations. It sets out to illustrate the variety of possible approaches to the main results, in order to initiate the reader to methods, the underlying reasoning, and fundamental ideas. It is suitable for both teaching and self-study. In his familiar, personal style, the author emphasizes ideas over calculations and, avoiding the condensed style frequently found in textbooks, explains these ideas without parsimony of words. The French edition in four volumes, published from 1998, has met with resounding success: the first two volumes are now available in English.
Download or read book Functional Analysis Holomorphy and Approximation Theory written by Guido I. Zapata and published by CRC Press. This book was released on 2020-12-22 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Differential Forms Orthogonal to Holomorphic Functions or Forms and Their Properties written by L a Aizenberg and published by American Mathematical Soc.. This book was released on 2000-04-30 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Extension of Holomorphic Functions written by Marek Jarnicki and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-05-05 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second extended edition of the classic reference on the extension problem of holomorphic functions in pluricomplex analysis contains a wealth of additional material, organized under the original chapter structure, and covers in a self-contained way all new and recent developments and theorems that appeared since the publication of the first edition about twenty years ago.
Download or read book Boundary Behavior of Holomorphic Functions of Several Complex Variables MN 11 written by Elias M. Stein and published by Princeton University Press. This book was released on 2015-03-08 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Application of Holomorphic Functions in Two and Higher Dimensions written by Klaus Gürlebeck and published by Springer. This book was released on 2016-06-20 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents applications of hypercomplex analysis to boundary value and initial-boundary value problems from various areas of mathematical physics. Given that quaternion and Clifford analysis offer natural and intelligent ways to enter into higher dimensions, it starts with quaternion and Clifford versions of complex function theory including series expansions with Appell polynomials, as well as Taylor and Laurent series. Several necessary function spaces are introduced, and an operator calculus based on modifications of the Dirac, Cauchy-Fueter, and Teodorescu operators and different decompositions of quaternion Hilbert spaces are proved. Finally, hypercomplex Fourier transforms are studied in detail. All this is then applied to first-order partial differential equations such as the Maxwell equations, the Carleman-Bers-Vekua system, the Schrödinger equation, and the Beltrami equation. The higher-order equations start with Riccati-type equations. Further topics include spatial fluid flow problems, image and multi-channel processing, image diffusion, linear scale invariant filtering, and others. One of the highlights is the derivation of the three-dimensional Kolosov-Mushkelishvili formulas in linear elasticity. Throughout the book the authors endeavor to present historical references and important personalities. The book is intended for a wide audience in the mathematical and engineering sciences and is accessible to readers with a basic grasp of real, complex, and functional analysis.
Download or read book Holomorphic Functions and Integral Representations in Several Complex Variables written by R. Michael Range and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Complex Analysis in Banach Spaces written by J. Mujica and published by Elsevier. This book was released on 1985-11-01 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: Problems arising from the study of holomorphic continuation and holomorphic approximation have been central in the development of complex analysis in finitely many variables, and constitute one of the most promising lines of research in infinite dimensional complex analysis. This book presents a unified view of these topics in both finite and infinite dimensions.
Download or read book Holomorphic Functions of Several Variables written by Ludger Kaup and published by Walter de Gruyter. This book was released on 2011-05-09 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob. Titles in planning include Mark M. Meerschaert, Alla Sikorskii, and Mohsen Zayernouri, Stochastic Models for Fractional Calculus, second edition (2018) Flavia Smarazzo and Alberto Tesei, Measure Theory: Radon Measures, Young Measures and Applications to Parabolic Problems (2019) Elena Cordero and Luigi Rodino, Time-Frequency Analysis of Operators (2019) Kezheng Li, Group Schemes and Their Actions (2019; together with Tsinghua University Press) Kai Liu, Ilpo Laine, and Lianzhong Yang, Complex Differential-Difference Equations (2021) Rajendra Vasant Gurjar, Kayo Masuda, and Masayoshi Miyanishi, Affine Space Fibrations (2022)
Download or read book From Holomorphic Functions to Complex Manifolds written by Klaus Fritzsche and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to the theory of complex manifolds covers the most important branches and methods in complex analysis of several variables while completely avoiding abstract concepts involving sheaves, coherence, and higher-dimensional cohomology. Only elementary methods such as power series, holomorphic vector bundles, and one-dimensional cocycles are used. Each chapter contains a variety of examples and exercises.
Download or read book Stein Manifolds and Holomorphic Mappings written by Franc Forstnerič and published by Springer Science & Business Media. This book was released on 2011-08-27 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main theme of this book is the homotopy principle for holomorphic mappings from Stein manifolds to the newly introduced class of Oka manifolds. The book contains the first complete account of Oka-Grauert theory and its modern extensions, initiated by Mikhail Gromov and developed in the last decade by the author and his collaborators. Included is the first systematic presentation of the theory of holomorphic automorphisms of complex Euclidean spaces, a survey on Stein neighborhoods, connections between the geometry of Stein surfaces and Seiberg-Witten theory, and a wide variety of applications ranging from classical to contemporary.
