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Author : H Begehr,Abduhamid Dzhuraev
Publisher : Chapman and Hall/CRC
Page : 464 pages
File Size : 45,5 Mb
Release : 1997-07-09
Category : Mathematics
ISBN : 0582255007
Author : So-chin Chen,Mei-Chi Shaw
Publisher : American Mathematical Soc.
Page : 396 pages
File Size : 48,5 Mb
Release : 2001
Category : Mathematics
ISBN : 0821829610
This book is intended as both an introductory text and a reference book for those interested in studying several complex variables in the context of partial differential equations. In the last few decades, significant progress has been made in the study of Cauchy-Riemann and tangential Cauchy-Riemann operators; this progress greatly influenced the development of PDEs and several complex variables. After the background material in complex analysis is developed in Chapters 1 to 3, thenext three chapters are devoted to the solvability and regularity of the Cauchy-Riemann equations using Hilbert space techniques. The authors provide a systematic study of the Cauchy-Riemann equations and the \bar\partial-Neumann problem, including Hórmander's L2 existence progress on the globalregularity and irregularity of the \bar\partial-Neumann operators. The second part of the book gives a comprehensive study of the tangential Cauchy-Riemann equations, another important class of equations in several complex variables first studied by Lewy. An up-to-date account of the L2 theory for \bar\partial b operator is given. Explicit integral solution representations are constructed both on the Heisenberg groups and on strictly convex boundaries with estimates in Hölder and L2spaces. Embeddability of abstract CR structures is discussed in detail here for the first time.Titles in this series are co-published with International Press, Cambridge, MA.
Author : Steven G. Krantz
Publisher : CRC Press
Page : 322 pages
File Size : 46,5 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9781351425803
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 : Heinrich G. W. Begehr
Publisher : Unknown
Page : 454 pages
File Size : 43,5 Mb
Release : 1995
Category : Differential equations, Partial
ISBN : OCLC:1090662170
Author : L. Hormander
Publisher : Elsevier
Page : 227 pages
File Size : 40,5 Mb
Release : 1973-02-12
Category : Mathematics
ISBN : 9780444105233
An Introduction to Complex Analysis in Several Variables
Author : H. Grauert,K. Fritzsche
Publisher : Springer Science & Business Media
Page : 213 pages
File Size : 49,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461298748
The present book grew out of introductory lectures on the theory offunctions of several variables. Its intent is to make the reader familiar, by the discussion of examples and special cases, with the most important branches and methods of this theory, among them, e.g., the problems of holomorphic continuation, the algebraic treatment of power series, sheaf and cohomology theory, and the real methods which stem from elliptic partial differential equations. In the first chapter we begin with the definition of holomorphic functions of several variables, their representation by the Cauchy integral, and their power series expansion on Reinhardt domains. It turns out that, in l:ontrast ~ 2 there exist domains G, G c en to the theory of a single variable, for n with G c G and G "# G such that each function holomorphic in G has a continuation on G. Domains G for which such a G does not exist are called domains of holomorphy. In Chapter 2 we give several characterizations of these domains of holomorphy (theorem of Cartan-Thullen, Levi's problem). We finally construct the holomorphic hull H(G} for each domain G, that is the largest (not necessarily schlicht) domain over en into which each function holomorphic on G can be continued.
Author : Michael Schneider,Yum-Tong Siu
Publisher : Cambridge University Press
Page : 582 pages
File Size : 46,8 Mb
Release : 1999
Category : Mathematics
ISBN : 0521770866
Expository articles on Several Complex Variables and its interactions with PDEs, algebraic geometry, number theory, and differential geometry, first published in 2000.
Author : Steven George Krantz
Publisher : American Mathematical Soc.
Page : 586 pages
File Size : 55,6 Mb
Release : 2001
Category : Functions of several complex variables
ISBN : 9780821827246
Emphasizing integral formulas, the geometric theory of pseudoconvexity, estimates, partial differential equations, approximation theory, inner functions, invariant metrics, and mapping theory, this title is intended for the student with a background in real and complex variable theory, harmonic analysis, and differential equations.
Author : Luis Barreira,Claudia Valls
Publisher : Springer Science & Business Media
Page : 417 pages
File Size : 54,7 Mb
Release : 2012-04-23
Category : Mathematics
ISBN : 9781447140085
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.
Author : Jiri Lebl
Publisher : Lulu.com
Page : 142 pages
File Size : 45,7 Mb
Release : 2016-05-05
Category : Electronic
ISBN : 9781365095573
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.
Author : Peter Ebenfelt,Norbert Hungerbühler,Joseph J. Kohn,Ngaiming Mok,Emil J. Straube
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 42,5 Mb
Release : 2011-01-30
Category : Mathematics
ISBN : 9783034600095
This volume presents the proceedings of a conference on Several Complex Variables, PDE’s, Geometry, and their interactions held in 2008 at the University of Fribourg, Switzerland, in honor of Linda Rothschild.
Author : Shiferaw Berhanu,Hua Chen,Jorge Hounie,Xiaojun Huang,Sheng-Li Tan,Stephen Shing-Toung Yau
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 47,8 Mb
Release : 2006
Category : Differential equations, Partial
ISBN : 9780821839218
The papers in this volume cover many important topics of current interest in partial differential equations and several complex variables. An international group of well-known mathematicians has contributed original research articles on diverse topics such as the geometry of complex manifolds, the mean curvature equation, formal solutions of singular partial differential equations, and complex vector fields. The material in this volume is useful for graduate students and researchers interested in partial differential equations and several complex variables.
Author : Einar Hille
Publisher : Courier Corporation
Page : 514 pages
File Size : 44,8 Mb
Release : 1997-01-01
Category : Mathematics
ISBN : 0486696200
Graduate-level text offers full treatments of existence theorems, representation of solutions by series, theory of majorants, dominants and minorants, questions of growth, much more. Includes 675 exercises. Bibliography.
Author : Paul M. Gauthier
Publisher : Springer
Page : 110 pages
File Size : 47,7 Mb
Release : 2014-11-07
Category : Mathematics
ISBN : 9783319115115
This monograph provides a concise, accessible snapshot of key topics in several complex variables, including the Cauchy Integral Formula, sequences of holomorphic functions, plurisubharmonic functions, the Dirichlet problem, and meromorphic functions. Based on a course given at Université de Montréal, this brief introduction covers areas of contemporary importance that are not mentioned in most treatments of the subject, such as modular forms, which are essential for Wiles' theorem and the unification of quantum theory and general relativity. Also covered is the Riemann manifold of a function, which generalizes the Riemann surface of a function of a single complex variable and is a topic that is well-known in one complex variable, but rarely treated in several variables. Many details, which are intentionally left out, as well as many theorems are stated as problems, providing students with carefully structured instructive exercises. Prerequisites for use of this book are functions of one complex variable, functions of several real variables, and topology, all at the undergraduate level. Lectures on Several Complex Variables will be of interest to advanced undergraduate and beginning undergraduate students, as well as mathematical researchers and professors.
Author : Henri Cartan
Publisher : Courier Corporation
Page : 242 pages
File Size : 49,5 Mb
Release : 2013-04-22
Category : Mathematics
ISBN : 9780486318677
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.
