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.
Review
"...third edition of this well-known, self-contained exposition of complex analysis from point of view of the theory of partial differential equations..." --Bulletin of the American Mathematical Society
"...this new edition ... remains a basic reference and compulsory reading for the new generations of complex analysts." --Revue Roumaine de Mathématiques Pures et Appliquées
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.
Review
"...third edition of this well-known, self-contained exposition of complex analysis from point of view of the theory of partial differential equations..." --Bulletin of the American Mathematical Society
"...this new edition ... remains a basic reference and compulsory reading for the new generations of complex analysts." --Revue Roumaine de Mathématiques Pures et Appliquées