|Statement||Robert C. Gunning, Hugo Rossi.|
|Series||Prentice Hall series in modern analysis|
|The Physical Object|
|Number of Pages||317|
The theory of functions of several complex variables is the branch of mathematics dealing with complex valued functions (,, ,)on the space C n of n-tuples of complex numbers. As in complex analysis, which is the case n = 1 but of a distinct character, these are not just any functions: they are supposed to be holomorphic or complex analytic, so that locally speaking they are power series in. functions and mapping of several complex variables and prove the n-dimensional chevreschevalaosta.comh-out this book n,m denote natural numbers (including zero). The set of strictly positive naturals will be denoted by N +, the set of strictly positive reals by R +. Can anyone recommend a good comprehensive introduction to functions of several complex variables that a) is fairly up to date, b) isn't a geometry or an algebra book only, but takes multiple viewpoints? I don't mind texts that require a lot of background as long as they present it intelligibly. Nov 25, · The later chapters give more detailed expositions of sheaf theory for analytic functions and the theory of complex analytic spaces. Since its original publication, this book has become a classic resource for the modern approach to functions of several complex variables and the theory of .
The purpose of this book is to present the classical analytic function theory of several variables as a standard subject in a course of mathematics after learning the elementary materials (sets, general topology, algebra, one complex variable). This includes the essential parts of Grauert–Remmert'sBrand: Springer Singapore. The later chapters give more detailed expositions of sheaf theory for analytic functions and the theory of complex analytic spaces. Since its original publication, this book has become a classic resource for the modern approach to functions of several complex variables and the theory of analytic spaces. Complex analytic functions are exactly equivalent to holomorphic functions, and are thus much more easily characterized.. For the case of an analytic function with several variables (see below), the real analyticity can be characterized using the Fourier–Bros–Iagolnitzer chevreschevalaosta.com third characterization has also a direct generalization for the multivariate case. Holomorphic functions Local rings of holomorphic functions Varieties Analytic sheaves Analytic spaces Cohomology theory Stein spaces, geometric theory Stein spaces, sheaf theory Pseudoconvexity Partitions of unity The theorem of Schwartz on Frechet spaces References Bibliography Index Analytic Functions of Several Complex Variables.
Mar 21, · This book explains results in the theory of functions of several complex variables which were mostly established from the late nineteenth century through the middle of the twentieth century. In the work, the author introduces the mathematical world created by his advisor, Kiyoshi Oka. In this volume, Oka's work is divided into two parts. More generally, a function of several complex variables that is square integrable over every compact subset of its domain is analytic if and only if it satisfies the Cauchy–Riemann equations in the sense of distributions. Functions of several complex variables are in some basic ways more complicated than functions of a single complex variable. The Theory of Functions of Several Complex Variables By B. Malgrange Notes by Raghavan Narasimhan 3 Complex analytic manifolds 19 4 Analytic Continuation 25 5 Envelopes of Holomorphy 29 equations to the case of functions of several variables). Jul 13, · chevreschevalaosta.com - Buy The Elementary Theory of Analytic Functions of One or Several Complex Variables (Dover Books on Mathematics) book online at best prices in India on chevreschevalaosta.com Read The Elementary Theory of Analytic Functions of One or Several Complex Variables (Dover Books on Mathematics) book reviews & author details and more at chevreschevalaosta.com Free delivery on qualified orders/5(2).