An Introduction to Complex Analysis in Several Variables

3rd Auflage
ISBN: 978-0-444-88446-6
Verlag: Elsevier Science & Technology

Buch, Englisch, 268 Seiten, Gewicht: 550 g

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.

Autoren/Hrsg.

Hormander, L.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe

Inhaltsverzeichnis

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