Laurent-Thiébaut C. Holomorphic Function Theory in Several Variables: An Introduction

London: Springer-Verlag, 2011. — 266 p.This book provides an introduction to complex analysis in several variables. The viewpoint of integral representation theory together with Grauert's bumping method offers a natural extension of single variable techniques to several variables analysis and leads rapidly to important global results. Applications focus on global extension problems for CR functions, such as the Hartogs-Bochner phenomenon and removable singularities for CR functions. Three appendices on differential manifolds, sheaf theory and functional analysis make the book self-contained.
Each chapter begins with a detailed abstract, clearly demonstrating the structure and relations of following chapters. New concepts are clearly defined and theorems and propositions are proved in detail. Historical notes are also provided at the end of each chapter.
Clear and succinct, this book will appeal to post-graduate students, young researchers seeking an introduction to holomorphic function theory in several variables and lecturers seeking a concise book on the subject.Elementary local properties of holomorphic functions of several complex variables
Currents and complex structures
The Bochner–Martinelli–Koppelman kernel and formula and applications
Extensions of CR functions
Extensions of holomorphic and CR functions on manifolds
Domains of holomorphy and pseudoconvexity
The Levi problem and the resolution of $$\overline{\partial}$$ in strictly pseudoconvex domains
Characterisation of removable singularities of CR functions on a strictly pseudoconvex boundary