Partial Differential Equations In Several Complex Variables

DOWNLOAD

Download Partial Differential Equations In Several Complex Variables PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Partial Differential Equations In Several Complex Variables book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page

Partial Differential Equations In Several Complex Variables

DOWNLOAD
Author : So-chin Chen
language : en
Publisher: American Mathematical Soc.
Release Date : 2001

Partial Differential Equations In Several Complex Variables written by So-chin Chen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.

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.

Partial Differential Equations And Complex Analysis

DOWNLOAD
Author : Steven G. Krantz
language : en
Publisher: CRC Press
Release Date : 2018-05-04

Partial Differential Equations And Complex Analysis written by Steven G. Krantz and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-04 with Mathematics categories.

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.

Several Complex Variables

DOWNLOAD
Author : H. Grauert
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Several Complex Variables written by H. Grauert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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.

Entire Functions Of Several Complex Variables

DOWNLOAD
Author : Pierre Lelong
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Entire Functions Of Several Complex Variables written by Pierre Lelong and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

I - Entire functions of several complex variables constitute an important and original chapter in complex analysis. The study is often motivated by certain applications to specific problems in other areas of mathematics: partial differential equations via the Fourier-Laplace transformation and convolution operators, analytic number theory and problems of transcen dence, or approximation theory, just to name a few. What is important for these applications is to find solutions which satisfy certain growth conditions. The specific problem defines inherently a growth scale, and one seeks a solution of the problem which satisfies certain growth conditions on this scale, and sometimes solutions of minimal asymp totic growth or optimal solutions in some sense. For one complex variable the study of solutions with growth conditions forms the core of the classical theory of entire functions and, historically, the relationship between the number of zeros of an entire function f(z) of one complex variable and the growth of If I (or equivalently log If I) was the first example of a systematic study of growth conditions in a general setting. Problems with growth conditions on the solutions demand much more precise information than existence theorems. The correspondence between two scales of growth can be interpreted often as a correspondence between families of bounded sets in certain Frechet spaces. However, for applications it is of utmost importance to develop precise and explicit representations of the solutions.

Fourier Analysis In Several Complex Variables

DOWNLOAD
Author : Leon Ehrenpreis
language : en
Publisher: Courier Corporation
Release Date : 2011-11-30

Fourier Analysis In Several Complex Variables written by Leon Ehrenpreis and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-30 with Mathematics categories.

Suitable for advanced undergraduates and graduate students, this text develops comparison theorems to establish the fundamentals of Fourier analysis and to illustrate their applications to partial differential equations. 1970 edition.

Geometric Analysis Of Pde And Several Complex Variables

DOWNLOAD
Author : Francois Treves
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

Geometric Analysis Of Pde And Several Complex Variables written by Francois Treves and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

This volume is dedicated to Francois Treves, who made substantial contributions to the geometric side of the theory of partial differential equations (PDEs) and several complex variables. One of his best-known contributions, reflected in many of the articles here, is the study of hypo-analytic structures. An international group of well-known mathematicians contributed to the volume. Articles generally reflect the interaction of geometry and analysis that is typical of Treves's work, such as the study of the special types of partial differential equations that arise in conjunction with CR-manifolds, symplectic geometry, or special families of vector fields. There are many topics in analysis and PDEs covered here, unified by their connections to geometry. The material is suitable for graduate students and research mathematicians interested in geometric analysis of PDEs and several complex variables.

Geometric Analysis Of Pdes And Several Complex Variables

DOWNLOAD
Author : Shiferaw Berhanu
language : en
Publisher: Springer Nature
Release Date : 2024-10-26

Geometric Analysis Of Pdes And Several Complex Variables written by Shiferaw Berhanu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-26 with Mathematics categories.

This volume convenes selected, peer-reviewed papers presented at the international workshop dedicated to Dr. Jorge Hounie on the occasion of his 75th birthday, held in Serra Negra, Brazil, from July 31 to August 4, 2023. The papers in this volume cover areas that include several complex variables, Cauchy-Riemann geometry, and partial differential equations. An Emeritus at the Federal University of São Carlos (UFScar), Brazil, Dr. Hounie has made significant contributions to partial differential equations, complex variables, harmonic analysis, and involutive structures. He has also been a kind and great mentor to numerous graduate students and postdocs who have gone on to pursue successful academic careers. Born in Bahia Blanca, Argentina, he completed his PhD studies at Rutgers University in 1974 and joined UFSCar as a Full Professor in 1995. He is a Full Member of the Brazilian Academy of Sciences. Within this book, readers will encounter a collection of cutting-edge research papers reflecting Dr. Hounie's research interests, valuable for both experienced researchers and graduate students alike.

Function Theory Of Several Complex Variables

DOWNLOAD
Author : Steven George Krantz
language : en
Publisher: American Mathematical Soc.
Release Date : 2001

Function Theory Of Several Complex Variables written by Steven George Krantz and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.

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.

Elementary Theory Of Analytic Functions Of One Or Several Complex Variables

DOWNLOAD
Author : Henri Cartan
language : en
Publisher: Courier Corporation
Release Date : 2013-04-22

Elementary Theory Of Analytic Functions Of One Or Several Complex Variables written by Henri Cartan and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-22 with Mathematics categories.

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.

Boundary Behavior Of Holomorphic Functions Of Several Complex Variables

DOWNLOAD
Author : Elias M. Stein
language : en
Publisher: Princeton University Press
Release Date : 2015-03-08

Boundary Behavior Of Holomorphic Functions Of Several Complex Variables written by Elias M. Stein and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-08 with Mathematics categories.

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.