Walter rudin, function theory in the unit ball of c n, springerverlag, 1980, mr601594. Function theory of several complex variables ams chelsea. Function theory of several complex variables ams ebooks. Elaine kehoe steven krantz appointed notices editor, pdf, notices ams, december 2009.
This new edition preserves the basic content and style of the earlier editions, the. The theory of several complex variables can be studied from several different perspectives. Complex analysis is fundamental in areas as diverse as. Authored by a ranking authority in harmonic analysis of several complex variables, this book embodies a stateoftheart entree at the intersection of two important fields of research. First, the complement of the closed set is open, and is thus the disjoint union of open intervals. Function theory of several complex variables, john wiley and. Krantz, function theory of several complex variables, john wiley and sons, new york, 1982. Function theory of several complex variables, 1992, 2nd edition 2001, american mathematical society, isbn 0821827243 complex analysis. The caratheodory and kobayashi metrics have proved to be important tools in the function theory of several complex variables.
Complex analysis in several variables, north holland 1973. Meichi shaw math 80350, topics in complex analysis fall 2020. Krantz was born in san francisco and raised in redwood city, california, in the. Function theory of one complex variable third edition robert e. Krantz graduate studies in mathematics volume 40 american mathematical society providence, rhode island. An elementary account of many aspects of classical complex function theory.
In this chapter, we shall define holomorphic functions of several complex variables. Function theory of one complex variable robert everist. Krantz has worked on the inhomogeneous cauchyriemann equations he obtained the first sharp estimates in a variety of nonisotropic norms, on separate smoothness of functions most notably with hypotheses about smoothness along integral curves of vector fields, on analysis on the heisenberg group and other nilpotent lie groups, on harmonic analysis in several complex variables, on the function theory of several complex variables, on the harmonic analysis of several real variables, on. Function theory of several complex variables, american mathemat.
Math 650 is a graduate course on several complex variables. Function theory of several complex variables wermer 1982. Applications of affine geometry to geometric function theory in several complex variables part i. Buy function theory of several complex variables ams chelsea publishing on free shipping on qualified orders function theory of several complex variables ams chelsea publishing. This is due to the traditionally strong position of the theory of plurisubharmonic functions in the institute. Published in mathematische annalen, volume 219, 1976, p. Krantz, function theory of several complex variables.
Partial differential equations and complex analysis explores the background and plumbs the depths of this symbiosis. Krantz ams chelseapublishing american mathematical society providence, rhode island. The book is an excellent introduction to a variety of topics. Harmonic and complex analysis in several variables. Function theory of several complex variables, steven george krantz, 2001, mathematics, 564 pages. Riemann surfaces, several complex variables, abelian functions, higher modular functions universitext eberhard freitag. One of the important results from complex variable theory discussed in chapter 17 is that if two formulas describe the same function of s everywhere on a line segment of finite length in the complex plane, either formula is a valid representation of that function for all complex s for which it converges this notion is the basic principle behind what is called analytic continuation. Krantz, function theory of several complex variables, wadsworth. Compact subset complex variable analytic continuation real hypersurface. However, the reader who gets maximum utility from the book will be that reader who has had a course in complex analysis at some time in his life. One of the remarkable features of this book is that it contains a large number of exercises and problems. The automorphism group of domains with boundary points of infinite type landucci, mario, illinois journal of mathematics, 2004.
Krantz, function theory of several complex variables, 2nd ed. Krantz breezy style is magnificent, but he never flinches from the details. Make sure to look at the current pdf, ive just updated it and added a few exercises. New york chichester weinheim brisbane singapore toronto. Pdf function theory of one complex variable semantic. Tasty bits of several complex variables a whirlwind tour of the subject jirilebl december23,2020 version3. Pdf the caratheodory and kobayashi metrics and applications. Lars hormander 1990 1966, an introduction to complex analysis in several variables 3rd ed. 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. Hassler whitney, complex analytic varieties, addisonwesley publishing co. Function theory of one complex variable volume 40 of graduate studies in mathematics, issn 10657339. G 2 holomorphic function, then fdoes not increase the corresponding caratheodorykobayashi distances. Krantz, function theory of several complex variables 1992 r. Krantz has worked on the inhomogeneous cauchyriemann equations he obtained the first sharp estimates in a variety of nonisotropic norms, on separate smoothness of functions most notably with hypotheses about smoothness along integral curves of vector fields, on analysis on the heisenberg group and other nilpotent lie groups, on harmonic analysis in several complex variables, on the function theory of several complex variables, on the harmonic analysis of several real variables.
But they are less familiar in the context of one complex variable. Krantz, function theory of several complex variables, second edition, 1992. Third edition graduate studies in mathematics by robert e. Gunning and hugo rossi, analytic functions of several complex variables, 1965. Proceedings of the summer research institute on several complex variables and com plex geometry, held at the university of california, santa cruz, santa cruz, california, july 1030, 1989t. Several complex variables with connections to algebraic. Functions of one complex variable, cauchy integral formula, taylor series, analytic continuation. Analytic polyhedra with noncompact automorphism group kim, kangtae, 2004. Theory of functions of a complex variable, second edition 3 vol. A remarkable theorem of hartogs see 2 tells us that a holomorphic function of several variables, defined as in the last paragraph, will be c. Harmonic and complex analysis in several variables steven g. The essentially local theory given in chapter 1, 3, 4 extends to these functions with little effort. Convergence of automorphisms and semicontinuity of. Krantz, s function theory of several complex variables, john wiley, new york.
Pdf function theory of one complex variable third edition. Complex scaling and domains with noncompact automorphism group kim, kangtae and krantz, steven g. Function theory of several complex variables wermer 1982 bulletin of the london mathematical society wiley online library. One complex variable from the several variables point of. Meichi shaw math 80350, topics in complex analysis fall.
Now a bit dated, this is the book from which everybody learned the subject half a century ago. Pdf function theory of one complex variable semantic scholar. Oct 22, 2020 in several complex variables the most convenient definition of holomorphic function is that it is a function that is holomorphic in the classical one variable sense in each variable separately. Function theory of one complex variable third edition. Its development started at the beginning of the twentieth century, from some important observations by poincar e and hartogs.
Written with the graduate student in mind, it is assumed that the reader has familiarity with the basics of complex analysis of one and several complex variables as well as with real and functional analysis. Greene, function theory of one complex variable isbn 0821839624. Function theory of several complex variables, amschelsea 1992 l. I know ive seen a large and organized pdf of his complex variables stuff, so one might think you could find the former somewhere as well. I see the elegant subject of complex function theory as a stage for the. One complex variable from the several variables point of view.
Gunning 2009 the theory of analytic functions of several complex variables enjoyed a. In complex analysis, the theory of functions of several complex variables is the branch of mathematics dealing with complex valued functions in the space c n of ntuples of complex numbers. Equation, riemann equation in one variable, functions of several complex variables. Function theory of several complex variables wermer 1982 bulletin of the london mathematical society. This is a nice textbook, which contains much more material than included in the course. I believe theres a really nice book by steven krantz called function theory of several complex variables. Sep 25, 2019 ever since the groundbreaking work of j. Function theory of several complex variables by krantz, steven g. Function theory of several complex variables wermer.
Function theory in several complex variables is fundamentally di erent from one complex variable. Bulletin new series of the american mathematical society. Michael range, holomorphic functions and integral representations in several complex variables, springer 1986, 1998. This book is a handy com pendium of all basic facts about complex variable theory. On each such interval, one can erect a little bump that vanishes to in. In this book, steven krantz approaches the subject from the point of view of a.
The purpose of this course is to study holomorphic function theory in several complex variables. Written with the graduate student in mind, it is assumed that the reader has familiarity with the basics of complex analysis of one and several complex variables as well as with real and. Gunning, hugo rossi, analytic functions of several complex variables, ams chelsea publishing. It is now understood that holomorphic functions of several complex variables are. Department of mathematics and statistics washington. Review of complex analysis in one variable and introduction to complex analysis in several variales.
Chapter 5 a glimpse of several complex variables pp. Fundamental concepts complex line integrals applications of the cauchy integral meromorphic functions and residues the zeros of a holomorphic function holomorphic functions as geometric mappings harmonic functions infinite series and products applications of infinite sums and products analytic continuation topology rational approximation theory special classes of holomorphic functions hilbert. Complex variable theory an overview sciencedirect topics. Function theory of several complex variables, 1992, 2nd edition 2001. Lecture notes several complex variables, pdf version. Elementary theory of analytic functions of one or several complex variables. We shall then prove two theorems which show that the behavior of functions of n complex variables, with n 1, is, in some ways, radically different from. While due homage is paid to the more traditional algebraic theory sheaves, cousin problems, etc. The complex numbers c consist of r2 equipped with some binary. Partial differential equations and complex analysis 1st. Narasimhan, several complex variables, university of chicago press, chicago, 1971. The rst chapter gives a nice summary of some of the ideas in the course. Lars hormander, an introduction to complex analysis in several variables, northholland. The geometric viewpoint, 2nd edition, mathematical association of america, carus mathematical monographs, 1990, 2004, isbn 0883850354.
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