In Hypo-Analytic Structures Franois Treves provides a systematic
approach to the study of the differential structures on manifolds
defined by systems of complex vector fields. Serving as his main
examples are the elliptic complexes, among which the De Rham and
Dolbeault are the best known, and the tangential Cauchy-Riemann
operators. Basic geometric entities attached to those structures
are isolated, such as maximally real submanifolds and orbits of the
system. Treves discusses the existence, uniqueness, and
approximation of local solutions to homogeneous and inhomogeneous
equations and delimits their supports. The contents of this book
consist of many results accumulated in the last decade by the
author and his collaborators, but also include classical results,
such as the Newlander-Nirenberg theorem. The reader will find an
elementary description of the FBI transform, as well as examples of
its use. Treves extends the main approximation and uniqueness
results to first-order nonlinear equations by means of the
Hamiltonian lift. Originally published in 1993. The Princeton
Legacy Library uses the latest print-on-demand technology to again
make available previously out-of-print books from the distinguished
backlist of Princeton University Press. These editions preserve the
original texts of these important books while presenting them in
durable paperback and hardcover editions. The goal of the Princeton
Legacy Library is to vastly increase access to the rich scholarly
heritage found in the thousands of books published by Princeton
University Press since its founding in 1905.
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