Hypo-Analytic Structures: Local Theory

Treves, François

ISBN 10: 069108744X / ISBN 13: 9780691087443

Published by Princeton University Press, 1993

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Bibliographic Details

• Title: Hypo-Analytic Structures: Local Theory
• Publisher: Princeton University Press
• Publication Date: 1993
• Language: English
• ISBN 10: 069108744X
• ISBN 13: 9780691087443
• Binding: Hardcover
• Condition: New

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Synopsis

In "Hypo-Analytic Structures" Francois 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 past 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.