The intention of gunning and rossis book is to provide an extensive introduction to the okacartan theory and some of its applications, and to the general theory. The theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century. Home analytic functions of several complex variables. Analytic functions of several complex variables ams chelsea. Gunning professor of mathematics princeton university mailing address. Analytic functions of several complex variables book. Functions of a complex variable, theory of encyclopedia of. Gunning and hugo rossi, analytic functions of several complex variables. Thus the subject of analytic continuation presents entirely new phenomena for n. Rossi analytic functions of several complex variables, prenticehall, englewood. Math 650 is a graduate course on several complex variables. Equation, riemann equation in one variable, functions of several complex variables pdf. There are different approaches to the concept of analyticity. Gunning, hugo rossi, analytic functions of several complex variables, ams chelsea publishing.
Gunning, hugo rossi free pdf d0wnl0ad, audio books, books to read, good books to read, cheap books, good books, online books, books online, book. Analytic functions of several complex variables ams. Topics in the function theory of compact riemann surfaces june 2007. I have always had a soft spot for gunning and rossi analytic functions of several complex variables, probably because it is more algebraic in its approach sheaves, local rings, and so on. Analytic functions of several complex variables book, 1965. Therefore,they are the centerpieces of the bulk of post19th century analysis and geometry and the tools of sheaf theory via commutative algebra are deeply interwoven in them. After recalling geometric and topological notions such as connectedness or convexity we will introduce holomorphic functions and mapping of several complex variables and prove the ndimensional. The emphasis in arranging the program was on the more. Analytic functions of several complex variables ams bookstore. Analytic continuation and boundary continuity of functions of several complex variables volume 89 issue 12 edgar lee stout. Zalcmans lemma and normality concerning shared values of holomorphic functions and their total derivatives in several complex variables liu, zhixue and cao, tingbin, rocky mountain journal of mathematics, 2019.
Robert clifford, 1931 analytic functions of several complex variables. Analytic functions of several complex variables robert gunning hugo rossi 1965. Several complex variables jaapkorevaar,janwiegerinck j. Analytic functions of several complex variables, by r. A function fz is said to be analytic in a region r of the complex plane if fz has a derivative at each point of r and. Analytic functions of several complex variables robert.
Recent development on grauert domains kan, sujen, 2004. Take a look at his treatment of domains of holomorphy in c1 contrasted with cn. Function theory of several complex variables ams chelsea. Hormanders introduction to complex analysis in several variables takes what i always thought was a more analytic approach. Robert clifford, 1931analytic functions of several complex variables.
Gunning, introduction to holomorphic functions of several variables steven g. Introduction to complex analysis in several variables. Rossi, analytic functions of several complex variables. Introduction to holomorphic functions of several variables, by robert. Gunning and hugo rossi, analytic functions of several complex variables, prenticehall inc. Functions of one complex variable, cauchy integral formula, taylor series, analytic continuation 2 cauchy integral formula cont.
Introduction to holomorphic functions of several variables, volume ii. After initial successes by poincare and others in the late 19th and early 20th centuries, the theory encountered obstacles that prevented it from growing quickly into an analogue of the theory for. This title intends to provide an extensive introduction to the okacartan theory and some of its applications, and to the general theory of analytic spaces. Now a bit dated, this is the book from which everybody learned the subject half a century ago. Gunning cochairman, david lieberman, james morrow, r. Lars hormander, an introduction to complex analysis in several variables, northholland publishing co. The material available in book form was presented well. Narasimhan, hugo rossi cochairman, yumtong siu, and r. As a result of all this,any pure approachsay,emphasizing analysisonly tells part. Analytic function theory of several variables book pdf download. It was in this academic atmosphere that i chose several. Analytic functions of several complex variables robert c. Princeton, gunning was lecturing from material in the book analytic functions of several complex variables that he wrote with rossi hugo rossi.
Gunning, princeton university, princeton, nj and hugo rossi, university of utah, salt lake city, ut. Several complex variables, perhaps more than most fields, seems to be a. To define an analytic function it is even sufficient that the convergent series 1 be given in a neighbourhood of a single point, for its values at another point and the corresponding series can be determined by the process of analytic continuation along various paths in the complex. Range, holomorphic functions and integral representations in several complex variables, springerverlag, berlin, 1986. The american mathematical society has reprinted the book analytic functions of several complex variables that hugo rossi and i wrote a number of years ago. Introduction to holomorphic functions of several variables. Complex analysis is the mathematical analysis of complexvalued analytic typically functions of a complex variable, of several complex. The theory of functions of several complex variables by b. Analytic functions of several complex variables about this title.
The book by gunning and rossi was the first of the modern era of the theory of several complex variables, which is distinguished by the use of these methods. The intention of gunning and rossi s book is to provide an extensive introduction to the okacartan theory and some of its applications, and to the general theory of analytic spaces. In 1990, the first author published a threevolume update titled introduction to holomorphic functions of several variables. Gunning and hugo rossi, analytic functions of several complex variables, 1965.
Analytic functions of several complex variables core. Make sure to look at the current pdf, ive just updated it and added a few. Gunning, robert c rossi, hugo 1965, analytic functions of several complex variables, prenticehall series in modern analysis, englewood. On the continuation of analytic curves springerlink. Analytic functions of several complex variables mathematical. I have tried to slog through gunning and rossi and have looked hard at hormander, but this looks like the best of the bunch. Analytic functions of several complex variables pdf free. Welcome,you are looking at books for reading, the several complex variables, you will able to read or download in pdf or epub books and notice some of author may have lock the live reading for some of country. Lars hormander, an introduction to complex analysis in several variables, northholland. Morsesard theorem for realanalytic functions dmlcz.
Zeros of analytic functions of several variables springerlink. Rossi, analytic functions of several complex variables, prenticehall series in modern analysis, prenticehall, englewood cliffs, nj, 1965. Good condition with no rips, writing, or highlighting on the pages. Lectures on the theory of functions of several complex variables. Pdf analytic function theory of several variables elements. The topic of the 1975 summer institute was the theory of functions of several complex variables. Loaded with examples and intuitive remarks, he helps the reader dig through the details of complex concepts. Fine hall, washington road, princeton, nj 08544 email. In this chapter we study the ndimensional complex vector space cn and introduce some notation used throughout this book.
Connections for a class of pseudogroup structures, proceedings of the conference on complex analysis, minneapolis, 1964, springerverlag, berlin, 1965, 186194. Lectures on the theory of functions of several complex. Analytic functions of several complex variables by robert c. Analytic continuation and boundary continuity of functions. After initial successes by poincare and others in the late 19th and early 20th centuries, the theory encountered obstacles that prevented it from growing quickly into an analogue of the theory.