Function theory of several complex variables

Function theory of several complex variables by Steven G. Krantz Download PDF EPUB FB2

While due homage is paid to the more traditional algebraic theory (sheaves, Cousin problems, etc.), the student with a background in real and complex variable theory, harmonic analysis, and differential equations will be most comfortable with this treatment.

It is currently the only book on the subject with exercises and a large number of by:   Title (HTML): Function Theory of Several Complex Variables: Second Edition Author(s) (Product display): Steven G. Krantz Affiliation(s) (HTML): Washington University, St. Louis, MO. Cartan's book starts with complex numbers, power series, and a review of the standard complex functions of one variable, e.g., the exponential, and the complex logarithm.

Then follow holomorphic functions, Taylor and Laurent expansions, singularities, Cauchy's theorems, residues, analytic continuation, lots of examples, and beautifully by: Functions of a Complex Variable: Theory and Technique makes available to readers a range of analytical techniques based upon complex variable theory.

It is a book in a special category of influential classics because it is based on the authors' extensive experience in modeling complicated situations and providing analytic by: Function Theory of Several Complex Variables.

This work departs from earlier treatments of the subject by emphasizing integral formulas, the geometric theory of pseudoconvexity, estimates, partial differential equations, approximation theory, the boundary behavior of holomorphic functions, inner functions, invariant metrics, and mapping theory.3/5(1).

The hardcover, and the book itself are good. We use it as a textbook; the content is sort of hard yet sufficient motivation is provided. I had this textbook during my first experience with Complex Analysis (or variables for that matter!).Cited by: This book is a short overview of the theory of several complex variables that emphasized the elementary aspects of the subject, such as Hartogs' theory, and domains of holomorphy.

The price quoted here for the book is surely a mistake, and even though it is out of print, Cited by:   The book concludes with several chapters on special topics, including full treatments of special functions, the prime number theorem, and the Bergman kernel.

The authors also treat \(H^p\) spaces and Painlevé's theorem on smoothness to the boundary for conformal maps. This book is a text for a first-year graduate course in complex on: Washington University, St.

Louis, MO. function of the 2n real variables x1,y1; ; xn,yn. Set, by definition, ∂f ∂zj = 1 2 ∂f ∂xj −i ∂f ∂yj. and ∂f ∂¯zj = 1 2 ∂f ∂xj +i ∂f ∂yj!.

Definition. f(z) is said to be holomorphic in Ω is ∂f ∂¯zj = 0, j = 1,n, at every point of Ω. (These equations generalize the Cauchy-Riemann equations to the case of functions of several variables).

FUNCTION THEORY OF SEVERAL COMPLEX VARIABLES SECOND EDITION BY STEVEN G. KRANTZ Review of the Classical Theory of Hp Spaces on the Boundary Values Pointwise Convergence for Harmonic Functions on Domains in RN Contents xi Boundary Values of Holomorphic Functions in Cn Admissible Convergence The Cited by: Notes for the course Function Theory of Several Complex Variables for the Ph.D.

program in Mathematics, at the Dipartimento di Matematica dell’Universit a di Milano, a.y. / FUNCTION THEORY OF SCV 1. The author provides explicit applications of holomprphic functions to quantum field theory and to different equations with constant coefficients, among other subjects.

Methods of the Theory of Functions of Several Complex Variables | The MIT Press. The book covers basic aspects of complex numbers, complex variables and complex functions.

It also deals with analytic functions, Laurent series etc. Contents. Introduction 9 Chapter 1. THE COMPLEX VARIABLE AND FUNCTIONS OF A COMPLEX VARIABLE Complex Numbers and Operations on Complex Numbers 11 a.

The concept of a complex number 11 b. The theory of functions of several complex variables is the branch of mathematics dealing with complex valued functions on the space Cn 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.

: Function theory of several complex variables (Pure and applied mathematics) () by Krantz, Steven G and a great selection of similar New, Used and Collectible Books available now at great prices/5(2). Theory of Analytic Functions of Several Complex Variables, Volume 1 Volume 8 of American Mathematical Society.

Translations of Mathematical Monographs Theory of Analytic Functions of Several Complex Variables Issue 8 of Translations of mathematical monographs: Author: Boris Abramovich Fuks: Publisher: American Mathematical Soc., ISBN.

functions and mapping of several complex variables and prove the n-dimensional h-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 +. 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 Oka-Cartan theory and some of its applications, and to the general theory of analytic on: University of Utah, Salt Lake City, UT.

Krantz has organized conferences, including the Summer Workshop in Several Complex Variables held in Santa Cruz in and attended by people. He was the principal lecturer at a CBMS conference at George Mason University in Alma mater: University of California at Santa.

Lorch’s proof of the spectral theorem from his book Spectral Theory. This has the flavor of complex analysis. The third proof due to Davies, presented at the end of Chapter XII replaces complex analysis by almost complex analysis.

The remaining chapters can be considered as giving more specialized in-File Size: 1MB. The theory of complex variables is significant in pure mathematics, and the basis for important applications in applied mathematics (e.g. fluids). This text provides an introduction to the ideas that are met at university: complex functions, differentiability, /5(11).

Topics in the theory of functions of several complex variables Item Preview remove-circle Topics in the theory of functions of several complex variables by Osgood, William F.

(William Fogg), Internet Archive Books. Scanned in China. Uploaded by Tracey Gutierres on November 5, SIMILAR ITEMS (based on metadata) Pages: Functions of a complex variable. This book is designed for students who, having acquired a good working knowledge of the calculus, desire to become acquainted with the theory of functions of a complex variable, and with the principal applications of that us examples have been given throughout the book, and there is also a set of Miscellaneous Examples, arranged to .