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Author : H Begehr
Publisher : Chapman and Hall/CRC
Page : 464 pages
File Size : 40,83 MB
Release : 1997-07-09
Category : Mathematics
ISBN : 9780582255005
Author : So-chin Chen
Publisher : American Mathematical Soc.
Page : 396 pages
File Size : 11,37 MB
Release : 2001
Category : Mathematics
ISBN : 9780821829615
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 : Heinrich G. W. Begehr
Publisher :
Page : 454 pages
File Size : 28,83 MB
Release : 1995
Category : Differential equations, Partial
ISBN :
Author : Steven G. Krantz
Publisher : CRC Press
Page : 322 pages
File Size : 44,35 MB
Release : 2018-05-04
Category : Mathematics
ISBN : 1351425803
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 : L. Hormander
Publisher : Elsevier
Page : 227 pages
File Size : 19,84 MB
Release : 1973-02-12
Category : Mathematics
ISBN : 0444105239
An Introduction to Complex Analysis in Several Variables
Author : Peter Ebenfelt
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 38,50 MB
Release : 2011-01-30
Category : Mathematics
ISBN : 3034600097
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 : H. Grauert
Publisher : Springer Science & Business Media
Page : 213 pages
File Size : 10,71 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461298741
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 : Steven George Krantz
Publisher : American Mathematical Soc.
Page : 586 pages
File Size : 36,43 MB
Release : 2001
Category : Mathematics
ISBN : 0821827243
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 : Robert Clifford Gunning
Publisher : American Mathematical Soc.
Page : 338 pages
File Size : 13,6 MB
Release : 2009
Category : Mathematics
ISBN : 0821821652
The theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century. This title intends to provide an extensive introduction to the Oka-Cartan theory and some of its applications, and to the general theory of analytic spaces.
Author : Luis Barreira
Publisher : Springer Science & Business Media
Page : 417 pages
File Size : 27,87 MB
Release : 2012-04-23
Category : Mathematics
ISBN : 1447140087
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.