Author: Mike Field
Publisher: Cambridge University Press
ISBN: 9780521288880
Category : Complex manifolds
Languages : en
Pages : 224
Book Description
Annotation This self-contained and relatively elementary introduction to functions of several complex variables and complex (especially compact) manifolds is intended to be a synthesis of those topics and a broad introduction to the field. Part I is suitable for advanced undergraduates and beginning postgraduates whilst Part II is written more for the graduate student. The work as a whole will be useful to professional mathematicians or mathematical physicists who wish to acquire a working knowledge of this area of mathematics. Many exercises have been included and indeed they form an integral part of the text. The prerequisites for understanding Part I would be met by any mathematics student with a first degree and together the two parts provide an introduction to the more advanced works in the subject.
Several Complex Variables and Complex Manifolds
Author: Mike Field
Publisher: Cambridge University Press
ISBN: 9780521288880
Category : Complex manifolds
Languages : en
Pages : 224
Book Description
Annotation This self-contained and relatively elementary introduction to functions of several complex variables and complex (especially compact) manifolds is intended to be a synthesis of those topics and a broad introduction to the field. Part I is suitable for advanced undergraduates and beginning postgraduates whilst Part II is written more for the graduate student. The work as a whole will be useful to professional mathematicians or mathematical physicists who wish to acquire a working knowledge of this area of mathematics. Many exercises have been included and indeed they form an integral part of the text. The prerequisites for understanding Part I would be met by any mathematics student with a first degree and together the two parts provide an introduction to the more advanced works in the subject.
Publisher: Cambridge University Press
ISBN: 9780521288880
Category : Complex manifolds
Languages : en
Pages : 224
Book Description
Annotation This self-contained and relatively elementary introduction to functions of several complex variables and complex (especially compact) manifolds is intended to be a synthesis of those topics and a broad introduction to the field. Part I is suitable for advanced undergraduates and beginning postgraduates whilst Part II is written more for the graduate student. The work as a whole will be useful to professional mathematicians or mathematical physicists who wish to acquire a working knowledge of this area of mathematics. Many exercises have been included and indeed they form an integral part of the text. The prerequisites for understanding Part I would be met by any mathematics student with a first degree and together the two parts provide an introduction to the more advanced works in the subject.
Several Complex Variables and Complex Manifolds I
Author: Mike Field
Publisher: Cambridge University Press
ISBN: 0521283019
Category : Mathematics
Languages : en
Pages : 209
Book Description
This self-contained and relatively elementary introduction to functions of several complex variables and complex (especially compact) manifolds was first published in 1982. It was intended be a synthesis of those topics and a broad introduction to the field. The work as a whole will be useful to professional mathematicians or mathematical physicists who wish to acquire a further knowledge of this area of mathematics. Many exercises have been included and indeed they form an integral part of the text. The prerequisites for understanding Part I would be met by any mathematics student with a first degree and together the two parts were designed to provide an introduction to the more advanced works in the subject.
Publisher: Cambridge University Press
ISBN: 0521283019
Category : Mathematics
Languages : en
Pages : 209
Book Description
This self-contained and relatively elementary introduction to functions of several complex variables and complex (especially compact) manifolds was first published in 1982. It was intended be a synthesis of those topics and a broad introduction to the field. The work as a whole will be useful to professional mathematicians or mathematical physicists who wish to acquire a further knowledge of this area of mathematics. Many exercises have been included and indeed they form an integral part of the text. The prerequisites for understanding Part I would be met by any mathematics student with a first degree and together the two parts were designed to provide an introduction to the more advanced works in the subject.
Several Complex Variables IV
Author: Semen G. Gindikin
Publisher: Springer Science & Business Media
ISBN: 3642612636
Category : Mathematics
Languages : en
Pages : 257
Book Description
This volume of the EMS contains four survey articles on analytic spaces. They are excellent introductions to each respective area. Starting from basic principles in several complex variables each article stretches out to current trends in research. Graduate students and researchers will find a useful addition in the extensive bibliography at the end of each article.
Publisher: Springer Science & Business Media
ISBN: 3642612636
Category : Mathematics
Languages : en
Pages : 257
Book Description
This volume of the EMS contains four survey articles on analytic spaces. They are excellent introductions to each respective area. Starting from basic principles in several complex variables each article stretches out to current trends in research. Graduate students and researchers will find a useful addition in the extensive bibliography at the end of each article.
Several Complex Variables VII
Author: H. Grauert
Publisher: Springer Science & Business Media
ISBN: 3662098733
Category : Mathematics
Languages : en
Pages : 374
Book Description
The first survey of its kind, written by internationally known, outstanding experts who developed substantial parts of the field. The book contains an introduction written by Remmert, describing the history of the subject, and is very useful to graduate students and researchers in complex analysis, algebraic geometry and differential geometry.
Publisher: Springer Science & Business Media
ISBN: 3662098733
Category : Mathematics
Languages : en
Pages : 374
Book Description
The first survey of its kind, written by internationally known, outstanding experts who developed substantial parts of the field. The book contains an introduction written by Remmert, describing the history of the subject, and is very useful to graduate students and researchers in complex analysis, algebraic geometry and differential geometry.
Several Complex Variables
Author: H. Grauert
Publisher: Springer Science & Business Media
ISBN: 1461298741
Category : Mathematics
Languages : en
Pages : 213
Book Description
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.
Publisher: Springer Science & Business Media
ISBN: 1461298741
Category : Mathematics
Languages : en
Pages : 213
Book Description
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.
Elementary Theory of Analytic Functions of One Or Several Complex Variables
Author: Henri Cartan
Publisher: Courier Corporation
ISBN: 0486685438
Category : Mathematics
Languages : en
Pages : 242
Book Description
Basic treatment of the theory of analytic functions of a complex variable, touching on analytic functions of several real or complex variables as well as the existence theorem for solutions of differential systems where data is analytic. Also included is a theory of abstract complex manifolds of one complex dimension; holomorphic functions; Cauchy's integral, more. Exercises. 1973 edition.
Publisher: Courier Corporation
ISBN: 0486685438
Category : Mathematics
Languages : en
Pages : 242
Book Description
Basic treatment of the theory of analytic functions of a complex variable, touching on analytic functions of several real or complex variables as well as the existence theorem for solutions of differential systems where data is analytic. Also included is a theory of abstract complex manifolds of one complex dimension; holomorphic functions; Cauchy's integral, more. Exercises. 1973 edition.
From Holomorphic Functions to Complex Manifolds
Author: Klaus Fritzsche
Publisher: Springer Science & Business Media
ISBN: 146849273X
Category : Mathematics
Languages : en
Pages : 406
Book Description
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.
Publisher: Springer Science & Business Media
ISBN: 146849273X
Category : Mathematics
Languages : en
Pages : 406
Book Description
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.
Several Complex Variables VI
Author: Reinhold Remmert
Publisher:
ISBN:
Category : Complex manifolds
Languages : en
Pages : 328
Book Description
Publisher:
ISBN:
Category : Complex manifolds
Languages : en
Pages : 328
Book Description
Partial Differential Equations in Several Complex Variables
Author: So-chin Chen
Publisher: American Mathematical Soc.
ISBN: 9780821829615
Category : Mathematics
Languages : en
Pages : 396
Book Description
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.
Publisher: American Mathematical Soc.
ISBN: 9780821829615
Category : Mathematics
Languages : en
Pages : 396
Book Description
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.
Several Complex Variables
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description