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.

An Introduction to Complex Analysis in Several Variables (Volume 7) (North-Holland Mathematical Library, Volume 7)

Science & Math

Hörmander, L.

Mathematics

North-Holland

An Introduction to Complex Analysis in Several Variables, Third Edition (North-Holland Mathematical Library)

Bounded analytic functions in the unit disk.- Strongly pseudoconvex manifolds.- Banach algebras and uniform approximation.- Extension of results from several complex variables to general function algebras.- The Cauchy problem for differential equations with constant coefficients.- Local Cauchy problem for linear partial differential equations with analytic coefficients.- Algebraic topology and operators in Hilbert space.- Deformations of Riemann surfaces.- Global stability questions in dynamical systems.

Lectures in Modern Analysis and Applications I (Lecture Notes in Mathematics, 103)

Atiyah, M.F.

Eells, J.

Hoffman, K. M.

Rickart, C. E.

Rossi, H.

Smale, S.

Treves, F.

Wermer, J.

Reference

Springer

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