An introduction to complex analysis in several variables
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Bibliographic Information
An introduction to complex analysis in several variables
（North-Holland mathematical library, v. 7）
North-Holland , Distributors for the United States and Canada, Elsevier Science, 1990
3rd rev. ed
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Note
Includes bibliographical references
Description and Table of Contents
Description
A number of monographs of various aspects of complex analysis in several variables have appeared since the first version of this book was published, but none of them uses the analytic techniques based on the solution of the Neumann Problem as the main tool.
The additions made in this third, revised edition place additional stress on results where these methods are particularly important. Thus, a section has been added presenting Ehrenpreis' ``fundamental principle'' in full. The local arguments in this section are closely related to the proof of the coherence of the sheaf of germs of functions vanishing on an analytic set. Also added is a discussion of the theorem of Siu on the Lelong numbers of plurisubharmonic functions. Since the L2 techniques are essential in the proof and plurisubharmonic functions play such an important role in this book, it seems natural to discuss their main singularities.
Table of Contents
I. Analytic Functions of One Complex Variable
II. Elementary Properties of Functions of Several Complex Variables
III. Applications to Commutative Banach Algebras
IV. L2 Estimates and Existence Theorems for the Operator
V. Stein Manifolds
VI. Local Properties of Analytic Functions
VII. Coherent Analytic Sheaves on Stein Manifolds. Bibliography
by "Nielsen BookData"
