UID:
almafu_9959240926602883
Format:
1 online resource (516 p.)
Edition:
Course Book
ISBN:
0-691-63541-2
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0-691-60670-6
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1-4008-6288-4
Series Statement:
Princeton Mathematical Series ; 214
Content:
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.
Note:
Description based upon print version of record.
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Frontmatter --
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Contents --
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Preface --
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I. Formally and Locally Integrable Structures. Basic Definitions --
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II. Local Approximation and Representation in Locally Integrable Structures --
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III. Hypo-Analytic Structures. Hypocomplex Manifolds --
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IV. Integrable Formal Structures. Normal Forms --
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V. Involutive Structures With Boundary --
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VI. Local Integraboity and Local Solvability in Elliptic Structures --
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VII. Examples of Nonintegrability and of Nonsolvability --
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VIII. Necessary Conditions for the Vanishing of the Cohomology. Local Solvability of a Single Vector Field --
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IX. FBI Transform in a Hypo-Analytic Manifold --
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X. Involutive Systems of Nonlinear First-Order Differential Equations --
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References --
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Index
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Issued also in print.
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English
Additional Edition:
ISBN 0-691-08744-X
Additional Edition:
ISBN 1-306-98561-7
Language:
English
DOI:
10.1515/9781400862887
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