Functions Of Several Complex Variables And Their Singularities

The book provides an introduction to the theory of functions of several complex variables and their singularities, with special emphasis on topological aspects. The topics include Riemann surfaces, holomorphic functions of several variables, classification and deformation of singularities, fundamentals of differential topology, and the topology of singularities. The aim of the book is to guide the reader from the fundamentals to more advanced topics of recent research. All the necessary prerequisites are specified and carefully explained. The general theory is illustrated by various examples and applications.

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.

The theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century. This title intends to provide an extensive introduction to the Oka-Cartan theory and some of its applications, and to the general theory of analytic spaces.

The complex variable and functions of a complex variable; Series of analytical functions; Analytic continuation elementary; The laurent series and isolated singular points; Residues and their applications; Conformal mapping; Analytic-functions in the solutions of boundary-value problems; Fundamentals of operational calculus; Saddle-point method; The wiener-hopf method; Functions of many complex variables.

Text contains sections on Singularities of analytic spaces, Function theory and real analysis, Compact complex manifolds, Survey papers